Lectures on Invariant Theory /:
This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2003.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
no. 296. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises. |
| Beschreibung: | Title from publishers bibliographic system (viewed 22 Dec 2011). |
| Beschreibung: | 1 online resource (236 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780511615436 0511615434 9780521525480 0521525489 9781107367173 1107367174 9781107362260 1107362261 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn776980318 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 090914s2003 enk ob 001 0 eng d | ||
| 040 | |a UkCbUP |b eng |e pn |c AUD |d OCLCO |d OCLCQ |d MHW |d EBLCP |d OCLCF |d DEBSZ |d OCLCQ |d YDXCP |d E7B |d N$T |d IDEBK |d OCLCQ |d AGLDB |d OCLCQ |d VTS |d BNG |d AU@ |d REC |d STF |d M8D |d UKAHL |d OCLCQ |d AJS |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d OCLCQ | ||
| 019 | |a 726827463 |a 976521260 |a 1167314228 | ||
| 020 | |a 9780511615436 |q (ebook) | ||
| 020 | |a 0511615434 |q (ebook) | ||
| 020 | |a 9780521525480 |q (paperback) | ||
| 020 | |a 0521525489 |q (paperback) | ||
| 020 | |a 9781107367173 | ||
| 020 | |a 1107367174 | ||
| 020 | |a 9781107362260 |q (electronic bk.) | ||
| 020 | |a 1107362261 |q (electronic bk.) | ||
| 035 | |a (OCoLC)776980318 |z (OCoLC)726827463 |z (OCoLC)976521260 |z (OCoLC)1167314228 | ||
| 050 | 4 | |a QA201 .D65 2002 | |
| 072 | 7 | |a MAT |x 002050 |2 bisacsh | |
| 082 | 7 | |a 512.5 |2 21 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Dolgachev, I. |q (Igor V.) |1 https://id.oclc.org/worldcat/entity/E39PBJyh68B9kPWfFMmXjx3qQq |0 http://id.loc.gov/authorities/names/n83216067 | |
| 245 | 1 | 0 | |a Lectures on Invariant Theory / |c Igor Dolgachev. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2003. | ||
| 300 | |a 1 online resource (236 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society Lecture Note Series ; |v no. 296 | |
| 500 | |a Title from publishers bibliographic system (viewed 22 Dec 2011). | ||
| 520 | |a This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Cover -- Title -- Copyright -- Dedication -- Preface -- Introduction -- 1 The symbolic method -- 1.1 First examples -- 1.2 Polarization and restitution -- 1.3 Bracket functions -- Bibliographical notes -- Exercises -- 2 The First Fundamental Theorem -- 2.1 The omega-operator -- 2.2 The proof -- 2.3 Grassmann varieties -- 2.4 The straightening algorithm -- Bibliographical notes -- Exercises -- 3 Reductive algebraic groups -- 3.1 The Gordan-Hilbert Theorem -- 3.2 The unitary trick -- 3.3 Affine algebraic groups -- 3.4 Nagata's Theorem -- Bibliographical notes -- Exercises. | |
| 505 | 8 | |a 4 Hilbert's Fourteenth Problem -- 4.1 The problem -- 4.2 The Weitzenb ock Theorem -- 4.3 Nagata's counterexample -- Bibliographical notes -- Exercises -- 5 Algebra of covariants -- 5.1 Examples of covariants -- 5.2 Covariants of an action -- 5.3 Linear representations of reductive groups -- 5.4 Dominant weights -- 5.5 The Cayley-Sylvester formula -- 5.6 Standard tableaux again -- Bibliographical notes -- Exercises -- 6 Quotients -- 6.1 Categorical and geometric quotients -- 6.2 Examples -- 6.3 Rational quotients -- Bibliographical notes -- Exercises -- 7 Linearization of actions. | |
| 505 | 8 | |a 7.1 Linearized line bundles -- 7.2 The existence of linearization -- 7.3 Linearization of an action -- Bibliographical notes -- Exercises -- 8 Stability -- 8.1 Stable points -- 8.2 The existence of a quotient -- 8.3 Examples -- Bibliographical notes -- Exercises -- 9 Numerical criterion of stability -- 9.1 The function æ(x, .) -- 9.2 The numerical criterion -- 9.3 The proof -- 9.4 The weight polytope -- 9.5 Kempf-stability -- Bibliographical notes -- Exercises -- 10 Projective hypersurfaces -- 10.1 Nonsingular hypersurfaces -- 10.2 Binary forms -- 10.3 Plane cubics -- 10.4 Cubic surfaces. | |
| 505 | 8 | |a Bibliographical notes -- Exercises -- 11 Configurations of linear subspaces -- 11.1 Stable configurations -- 11.2 Points in Pn -- 11.3 Lines in P3 -- Bibliographical notes -- Exercises -- 12 Toric varieties -- 12.1 Actions of a torus on an affine space -- 12.2 Fans -- 12.3 Examples -- Bibliographical notes -- Exercises -- Bibliography -- Index of Notation -- Index. | |
| 650 | 0 | |a Invariants. |0 http://id.loc.gov/authorities/subjects/sh85067665 | |
| 650 | 0 | |a Linear algebraic groups. |0 http://id.loc.gov/authorities/subjects/sh85077171 | |
| 650 | 0 | |a Geometry, Differential. |0 http://id.loc.gov/authorities/subjects/sh85054146 | |
| 650 | 0 | |a Geometry, Algebraic. |0 http://id.loc.gov/authorities/subjects/sh85054140 | |
| 650 | 6 | |a Invariants. | |
| 650 | 6 | |a Groupes linéaires algébriques. | |
| 650 | 6 | |a Géométrie différentielle. | |
| 650 | 6 | |a Géométrie algébrique. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Geometry, Algebraic |2 fast | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 650 | 7 | |a Invariants |2 fast | |
| 650 | 7 | |a Linear algebraic groups |2 fast | |
| 776 | 0 | 8 | |i Print version: |z 9780521525480 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v no. 296. |0 http://id.loc.gov/authorities/names/n42015587 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551344 |3 Volltext |
| 936 | |a BATCHLOAD | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH13427009 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH26478479 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1182506 | ||
| 938 | |a ebrary |b EBRY |n ebr10461595 | ||
| 938 | |a EBSCOhost |b EBSC |n 551344 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis25158818 | ||
| 938 | |a YBP Library Services |b YANK |n 10689732 | ||
| 938 | |a YBP Library Services |b YANK |n 10370373 | ||
| 938 | |a YBP Library Services |b YANK |n 3279063 | ||
| 938 | |a YBP Library Services |b YANK |n 10374348 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn776980318 |
|---|---|
| _version_ | 1816881786574077952 |
| adam_text | |
| any_adam_object | |
| author | Dolgachev, I. (Igor V.) |
| author_GND | http://id.loc.gov/authorities/names/n83216067 |
| author_facet | Dolgachev, I. (Igor V.) |
| author_role | |
| author_sort | Dolgachev, I. |
| author_variant | i d id |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA201 |
| callnumber-raw | QA201 .D65 2002 |
| callnumber-search | QA201 .D65 2002 |
| callnumber-sort | QA 3201 D65 42002 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover -- Title -- Copyright -- Dedication -- Preface -- Introduction -- 1 The symbolic method -- 1.1 First examples -- 1.2 Polarization and restitution -- 1.3 Bracket functions -- Bibliographical notes -- Exercises -- 2 The First Fundamental Theorem -- 2.1 The omega-operator -- 2.2 The proof -- 2.3 Grassmann varieties -- 2.4 The straightening algorithm -- Bibliographical notes -- Exercises -- 3 Reductive algebraic groups -- 3.1 The Gordan-Hilbert Theorem -- 3.2 The unitary trick -- 3.3 Affine algebraic groups -- 3.4 Nagata's Theorem -- Bibliographical notes -- Exercises. 4 Hilbert's Fourteenth Problem -- 4.1 The problem -- 4.2 The Weitzenb ock Theorem -- 4.3 Nagata's counterexample -- Bibliographical notes -- Exercises -- 5 Algebra of covariants -- 5.1 Examples of covariants -- 5.2 Covariants of an action -- 5.3 Linear representations of reductive groups -- 5.4 Dominant weights -- 5.5 The Cayley-Sylvester formula -- 5.6 Standard tableaux again -- Bibliographical notes -- Exercises -- 6 Quotients -- 6.1 Categorical and geometric quotients -- 6.2 Examples -- 6.3 Rational quotients -- Bibliographical notes -- Exercises -- 7 Linearization of actions. 7.1 Linearized line bundles -- 7.2 The existence of linearization -- 7.3 Linearization of an action -- Bibliographical notes -- Exercises -- 8 Stability -- 8.1 Stable points -- 8.2 The existence of a quotient -- 8.3 Examples -- Bibliographical notes -- Exercises -- 9 Numerical criterion of stability -- 9.1 The function æ(x, .) -- 9.2 The numerical criterion -- 9.3 The proof -- 9.4 The weight polytope -- 9.5 Kempf-stability -- Bibliographical notes -- Exercises -- 10 Projective hypersurfaces -- 10.1 Nonsingular hypersurfaces -- 10.2 Binary forms -- 10.3 Plane cubics -- 10.4 Cubic surfaces. Bibliographical notes -- Exercises -- 11 Configurations of linear subspaces -- 11.1 Stable configurations -- 11.2 Points in Pn -- 11.3 Lines in P3 -- Bibliographical notes -- Exercises -- 12 Toric varieties -- 12.1 Actions of a torus on an affine space -- 12.2 Fans -- 12.3 Examples -- Bibliographical notes -- Exercises -- Bibliography -- Index of Notation -- Index. |
| ctrlnum | (OCoLC)776980318 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05610cam a2200793 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn776980318</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr |||||||||||</controlfield><controlfield tag="008">090914s2003 enk ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">UkCbUP</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">AUD</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MHW</subfield><subfield code="d">EBLCP</subfield><subfield code="d">OCLCF</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">E7B</subfield><subfield code="d">N$T</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">BNG</subfield><subfield code="d">AU@</subfield><subfield code="d">REC</subfield><subfield code="d">STF</subfield><subfield code="d">M8D</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">726827463</subfield><subfield code="a">976521260</subfield><subfield code="a">1167314228</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511615436</subfield><subfield code="q">(ebook)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511615434</subfield><subfield code="q">(ebook)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521525480</subfield><subfield code="q">(paperback)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521525489</subfield><subfield code="q">(paperback)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107367173</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107367174</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107362260</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107362261</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)776980318</subfield><subfield code="z">(OCoLC)726827463</subfield><subfield code="z">(OCoLC)976521260</subfield><subfield code="z">(OCoLC)1167314228</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA201 .D65 2002</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">002050</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">512.5</subfield><subfield code="2">21</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dolgachev, I.</subfield><subfield code="q">(Igor V.)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJyh68B9kPWfFMmXjx3qQq</subfield><subfield code="0">http://id.loc.gov/authorities/names/n83216067</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lectures on Invariant Theory /</subfield><subfield code="c">Igor Dolgachev.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2003.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (236 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">London Mathematical Society Lecture Note Series ;</subfield><subfield code="v">no. 296</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publishers bibliographic system (viewed 22 Dec 2011).</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover -- Title -- Copyright -- Dedication -- Preface -- Introduction -- 1 The symbolic method -- 1.1 First examples -- 1.2 Polarization and restitution -- 1.3 Bracket functions -- Bibliographical notes -- Exercises -- 2 The First Fundamental Theorem -- 2.1 The omega-operator -- 2.2 The proof -- 2.3 Grassmann varieties -- 2.4 The straightening algorithm -- Bibliographical notes -- Exercises -- 3 Reductive algebraic groups -- 3.1 The Gordan-Hilbert Theorem -- 3.2 The unitary trick -- 3.3 Affine algebraic groups -- 3.4 Nagata's Theorem -- Bibliographical notes -- Exercises.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4 Hilbert's Fourteenth Problem -- 4.1 The problem -- 4.2 The Weitzenb ock Theorem -- 4.3 Nagata's counterexample -- Bibliographical notes -- Exercises -- 5 Algebra of covariants -- 5.1 Examples of covariants -- 5.2 Covariants of an action -- 5.3 Linear representations of reductive groups -- 5.4 Dominant weights -- 5.5 The Cayley-Sylvester formula -- 5.6 Standard tableaux again -- Bibliographical notes -- Exercises -- 6 Quotients -- 6.1 Categorical and geometric quotients -- 6.2 Examples -- 6.3 Rational quotients -- Bibliographical notes -- Exercises -- 7 Linearization of actions.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">7.1 Linearized line bundles -- 7.2 The existence of linearization -- 7.3 Linearization of an action -- Bibliographical notes -- Exercises -- 8 Stability -- 8.1 Stable points -- 8.2 The existence of a quotient -- 8.3 Examples -- Bibliographical notes -- Exercises -- 9 Numerical criterion of stability -- 9.1 The function æ(x, .) -- 9.2 The numerical criterion -- 9.3 The proof -- 9.4 The weight polytope -- 9.5 Kempf-stability -- Bibliographical notes -- Exercises -- 10 Projective hypersurfaces -- 10.1 Nonsingular hypersurfaces -- 10.2 Binary forms -- 10.3 Plane cubics -- 10.4 Cubic surfaces.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Bibliographical notes -- Exercises -- 11 Configurations of linear subspaces -- 11.1 Stable configurations -- 11.2 Points in Pn -- 11.3 Lines in P3 -- Bibliographical notes -- Exercises -- 12 Toric varieties -- 12.1 Actions of a torus on an affine space -- 12.2 Fans -- 12.3 Examples -- Bibliographical notes -- Exercises -- Bibliography -- Index of Notation -- Index.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Invariants.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85067665</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Linear algebraic groups.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85077171</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Geometry, Differential.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85054146</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Geometry, Algebraic.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85054140</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Invariants.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Groupes linéaires algébriques.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Géométrie différentielle.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Géométrie algébrique.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Algebra</subfield><subfield code="x">Linear.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometry, Algebraic</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometry, Differential</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Invariants</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Linear algebraic groups</subfield><subfield code="2">fast</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="z">9780521525480</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society lecture note series ;</subfield><subfield code="v">no. 296.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n42015587</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551344</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="936" ind1=" " ind2=" "><subfield code="a">BATCHLOAD</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH13427009</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH26478479</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1182506</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10461595</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">551344</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">cis25158818</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">10689732</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">10370373</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3279063</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">10374348</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn776980318 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:15Z |
| institution | BVB |
| isbn | 9780511615436 0511615434 9780521525480 0521525489 9781107367173 1107367174 9781107362260 1107362261 |
| language | English |
| oclc_num | 776980318 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (236 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society Lecture Note Series ; |
| spelling | Dolgachev, I. (Igor V.) https://id.oclc.org/worldcat/entity/E39PBJyh68B9kPWfFMmXjx3qQq http://id.loc.gov/authorities/names/n83216067 Lectures on Invariant Theory / Igor Dolgachev. Cambridge : Cambridge University Press, 2003. 1 online resource (236 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society Lecture Note Series ; no. 296 Title from publishers bibliographic system (viewed 22 Dec 2011). This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises. Includes bibliographical references and index. Cover -- Title -- Copyright -- Dedication -- Preface -- Introduction -- 1 The symbolic method -- 1.1 First examples -- 1.2 Polarization and restitution -- 1.3 Bracket functions -- Bibliographical notes -- Exercises -- 2 The First Fundamental Theorem -- 2.1 The omega-operator -- 2.2 The proof -- 2.3 Grassmann varieties -- 2.4 The straightening algorithm -- Bibliographical notes -- Exercises -- 3 Reductive algebraic groups -- 3.1 The Gordan-Hilbert Theorem -- 3.2 The unitary trick -- 3.3 Affine algebraic groups -- 3.4 Nagata's Theorem -- Bibliographical notes -- Exercises. 4 Hilbert's Fourteenth Problem -- 4.1 The problem -- 4.2 The Weitzenb ock Theorem -- 4.3 Nagata's counterexample -- Bibliographical notes -- Exercises -- 5 Algebra of covariants -- 5.1 Examples of covariants -- 5.2 Covariants of an action -- 5.3 Linear representations of reductive groups -- 5.4 Dominant weights -- 5.5 The Cayley-Sylvester formula -- 5.6 Standard tableaux again -- Bibliographical notes -- Exercises -- 6 Quotients -- 6.1 Categorical and geometric quotients -- 6.2 Examples -- 6.3 Rational quotients -- Bibliographical notes -- Exercises -- 7 Linearization of actions. 7.1 Linearized line bundles -- 7.2 The existence of linearization -- 7.3 Linearization of an action -- Bibliographical notes -- Exercises -- 8 Stability -- 8.1 Stable points -- 8.2 The existence of a quotient -- 8.3 Examples -- Bibliographical notes -- Exercises -- 9 Numerical criterion of stability -- 9.1 The function æ(x, .) -- 9.2 The numerical criterion -- 9.3 The proof -- 9.4 The weight polytope -- 9.5 Kempf-stability -- Bibliographical notes -- Exercises -- 10 Projective hypersurfaces -- 10.1 Nonsingular hypersurfaces -- 10.2 Binary forms -- 10.3 Plane cubics -- 10.4 Cubic surfaces. Bibliographical notes -- Exercises -- 11 Configurations of linear subspaces -- 11.1 Stable configurations -- 11.2 Points in Pn -- 11.3 Lines in P3 -- Bibliographical notes -- Exercises -- 12 Toric varieties -- 12.1 Actions of a torus on an affine space -- 12.2 Fans -- 12.3 Examples -- Bibliographical notes -- Exercises -- Bibliography -- Index of Notation -- Index. Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Linear algebraic groups. http://id.loc.gov/authorities/subjects/sh85077171 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Invariants. Groupes linéaires algébriques. Géométrie différentielle. Géométrie algébrique. MATHEMATICS Algebra Linear. bisacsh Geometry, Algebraic fast Geometry, Differential fast Invariants fast Linear algebraic groups fast Print version: 9780521525480 London Mathematical Society lecture note series ; no. 296. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551344 Volltext |
| spellingShingle | Dolgachev, I. (Igor V.) Lectures on Invariant Theory / London Mathematical Society lecture note series ; Cover -- Title -- Copyright -- Dedication -- Preface -- Introduction -- 1 The symbolic method -- 1.1 First examples -- 1.2 Polarization and restitution -- 1.3 Bracket functions -- Bibliographical notes -- Exercises -- 2 The First Fundamental Theorem -- 2.1 The omega-operator -- 2.2 The proof -- 2.3 Grassmann varieties -- 2.4 The straightening algorithm -- Bibliographical notes -- Exercises -- 3 Reductive algebraic groups -- 3.1 The Gordan-Hilbert Theorem -- 3.2 The unitary trick -- 3.3 Affine algebraic groups -- 3.4 Nagata's Theorem -- Bibliographical notes -- Exercises. 4 Hilbert's Fourteenth Problem -- 4.1 The problem -- 4.2 The Weitzenb ock Theorem -- 4.3 Nagata's counterexample -- Bibliographical notes -- Exercises -- 5 Algebra of covariants -- 5.1 Examples of covariants -- 5.2 Covariants of an action -- 5.3 Linear representations of reductive groups -- 5.4 Dominant weights -- 5.5 The Cayley-Sylvester formula -- 5.6 Standard tableaux again -- Bibliographical notes -- Exercises -- 6 Quotients -- 6.1 Categorical and geometric quotients -- 6.2 Examples -- 6.3 Rational quotients -- Bibliographical notes -- Exercises -- 7 Linearization of actions. 7.1 Linearized line bundles -- 7.2 The existence of linearization -- 7.3 Linearization of an action -- Bibliographical notes -- Exercises -- 8 Stability -- 8.1 Stable points -- 8.2 The existence of a quotient -- 8.3 Examples -- Bibliographical notes -- Exercises -- 9 Numerical criterion of stability -- 9.1 The function æ(x, .) -- 9.2 The numerical criterion -- 9.3 The proof -- 9.4 The weight polytope -- 9.5 Kempf-stability -- Bibliographical notes -- Exercises -- 10 Projective hypersurfaces -- 10.1 Nonsingular hypersurfaces -- 10.2 Binary forms -- 10.3 Plane cubics -- 10.4 Cubic surfaces. Bibliographical notes -- Exercises -- 11 Configurations of linear subspaces -- 11.1 Stable configurations -- 11.2 Points in Pn -- 11.3 Lines in P3 -- Bibliographical notes -- Exercises -- 12 Toric varieties -- 12.1 Actions of a torus on an affine space -- 12.2 Fans -- 12.3 Examples -- Bibliographical notes -- Exercises -- Bibliography -- Index of Notation -- Index. Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Linear algebraic groups. http://id.loc.gov/authorities/subjects/sh85077171 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Invariants. Groupes linéaires algébriques. Géométrie différentielle. Géométrie algébrique. MATHEMATICS Algebra Linear. bisacsh Geometry, Algebraic fast Geometry, Differential fast Invariants fast Linear algebraic groups fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85067665 http://id.loc.gov/authorities/subjects/sh85077171 http://id.loc.gov/authorities/subjects/sh85054146 http://id.loc.gov/authorities/subjects/sh85054140 |
| title | Lectures on Invariant Theory / |
| title_auth | Lectures on Invariant Theory / |
| title_exact_search | Lectures on Invariant Theory / |
| title_full | Lectures on Invariant Theory / Igor Dolgachev. |
| title_fullStr | Lectures on Invariant Theory / Igor Dolgachev. |
| title_full_unstemmed | Lectures on Invariant Theory / Igor Dolgachev. |
| title_short | Lectures on Invariant Theory / |
| title_sort | lectures on invariant theory |
| topic | Invariants. http://id.loc.gov/authorities/subjects/sh85067665 Linear algebraic groups. http://id.loc.gov/authorities/subjects/sh85077171 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Invariants. Groupes linéaires algébriques. Géométrie différentielle. Géométrie algébrique. MATHEMATICS Algebra Linear. bisacsh Geometry, Algebraic fast Geometry, Differential fast Invariants fast Linear algebraic groups fast |
| topic_facet | Invariants. Linear algebraic groups. Geometry, Differential. Geometry, Algebraic. Groupes linéaires algébriques. Géométrie différentielle. Géométrie algébrique. MATHEMATICS Algebra Linear. Geometry, Algebraic Geometry, Differential Invariants Linear algebraic groups |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551344 |
| work_keys_str_mv | AT dolgachevi lecturesoninvarianttheory |