Cohomology of vector bundles and syzygies /:
The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2003.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
149. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method. |
| Beschreibung: | 1 online resource (xiv, 371 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 359-366) and indexes. |
| ISBN: | 0511066015 9780511066016 0511546556 9780511546556 0511308469 9780511308468 1107127793 9781107127791 1280417382 9781280417382 9786610417384 6610417385 0511169639 9780511169632 0511205600 9780511205606 |
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| 245 | 1 | 0 | |a Cohomology of vector bundles and syzygies / |c Jerzy Weyman. |
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |g 1. |t Introductory Material -- |g 2. |t Schur Functors and Schur Complexes -- |g 3. |t Grassmannians and Flag Varieties -- |g 4. |t Bott's Theorem -- |g 5. |t The Geometric Technique -- |g 6. |t The Determinantal Varieties -- |g 7. |t Higher Rank Varieties -- |g 8. |t The Nilpotent Orbit Closures -- |g 9. |t Resultants and Discriminants. |
| 520 | |a The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method. | ||
| 546 | |a English. | ||
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| 650 | 0 | |a Homology theory. |0 http://id.loc.gov/authorities/subjects/sh85061770 | |
| 650 | 6 | |a Syzygies (Mathématiques) | |
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Datensatz im Suchindex
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| _version_ | 1816881623369515008 |
| adam_text | |
| any_adam_object | |
| author | Weyman, Jerzy, 1955- |
| author_GND | http://id.loc.gov/authorities/names/n2002158812 |
| author_facet | Weyman, Jerzy, 1955- |
| author_role | |
| author_sort | Weyman, Jerzy, 1955- |
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| collection | ZDB-4-EBA |
| contents | Introductory Material -- Schur Functors and Schur Complexes -- Grassmannians and Flag Varieties -- Bott's Theorem -- The Geometric Technique -- The Determinantal Varieties -- Higher Rank Varieties -- The Nilpotent Orbit Closures -- Resultants and Discriminants. |
| ctrlnum | (OCoLC)57300141 |
| 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 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocm57300141 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:15:40Z |
| institution | BVB |
| isbn | 0511066015 9780511066016 0511546556 9780511546556 0511308469 9780511308468 1107127793 9781107127791 1280417382 9781280417382 9786610417384 6610417385 0511169639 9780511169632 0511205600 9780511205606 |
| language | English |
| oclc_num | 57300141 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 371 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Cambridge tracts in mathematics ; |
| series2 | Cambridge tracts in mathematics ; |
| spelling | Weyman, Jerzy, 1955- https://id.oclc.org/worldcat/entity/E39PCjwft8YXrrgVWbK7vgm6Dm http://id.loc.gov/authorities/names/n2002158812 Cohomology of vector bundles and syzygies / Jerzy Weyman. Cambridge ; New York : Cambridge University Press, 2003. 1 online resource (xiv, 371 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 149 Includes bibliographical references (pages 359-366) and indexes. Print version record. 1. Introductory Material -- 2. Schur Functors and Schur Complexes -- 3. Grassmannians and Flag Varieties -- 4. Bott's Theorem -- 5. The Geometric Technique -- 6. The Determinantal Varieties -- 7. Higher Rank Varieties -- 8. The Nilpotent Orbit Closures -- 9. Resultants and Discriminants. The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method. English. Syzygies (Mathematics) http://id.loc.gov/authorities/subjects/sh85131751 Vector bundles. http://id.loc.gov/authorities/subjects/sh85142450 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Syzygies (Mathématiques) Fibrés vectoriels. Homologie. MATHEMATICS Algebra Linear. bisacsh Homology theory. cct Syzygies (Mathematics) cct Vector bundles. cct Homology theory fast Syzygies (Mathematics) fast Vector bundles fast Syzygie gnd http://d-nb.info/gnd/4326483-9 Kommutative Algebra gnd http://d-nb.info/gnd/4164821-3 Vektorraumbündel gnd http://d-nb.info/gnd/4187470-5 Kohomologietheorie gnd http://d-nb.info/gnd/4164610-1 Electronic books. Print version: Weyman, Jerzy, 1955- Cohomology of vector bundles and syzygies. Cambridge ; New York : Cambridge University Press, 2003 0521621976 (DLC) 2002074071 (OCoLC)50252085 Cambridge tracts in mathematics ; 149. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=120694 Volltext |
| spellingShingle | Weyman, Jerzy, 1955- Cohomology of vector bundles and syzygies / Cambridge tracts in mathematics ; Introductory Material -- Schur Functors and Schur Complexes -- Grassmannians and Flag Varieties -- Bott's Theorem -- The Geometric Technique -- The Determinantal Varieties -- Higher Rank Varieties -- The Nilpotent Orbit Closures -- Resultants and Discriminants. Syzygies (Mathematics) http://id.loc.gov/authorities/subjects/sh85131751 Vector bundles. http://id.loc.gov/authorities/subjects/sh85142450 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Syzygies (Mathématiques) Fibrés vectoriels. Homologie. MATHEMATICS Algebra Linear. bisacsh Homology theory. cct Syzygies (Mathematics) cct Vector bundles. cct Homology theory fast Syzygies (Mathematics) fast Vector bundles fast Syzygie gnd http://d-nb.info/gnd/4326483-9 Kommutative Algebra gnd http://d-nb.info/gnd/4164821-3 Vektorraumbündel gnd http://d-nb.info/gnd/4187470-5 Kohomologietheorie gnd http://d-nb.info/gnd/4164610-1 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85131751 http://id.loc.gov/authorities/subjects/sh85142450 http://id.loc.gov/authorities/subjects/sh85061770 http://d-nb.info/gnd/4326483-9 http://d-nb.info/gnd/4164821-3 http://d-nb.info/gnd/4187470-5 http://d-nb.info/gnd/4164610-1 |
| title | Cohomology of vector bundles and syzygies / |
| title_alt | Introductory Material -- Schur Functors and Schur Complexes -- Grassmannians and Flag Varieties -- Bott's Theorem -- The Geometric Technique -- The Determinantal Varieties -- Higher Rank Varieties -- The Nilpotent Orbit Closures -- Resultants and Discriminants. |
| title_auth | Cohomology of vector bundles and syzygies / |
| title_exact_search | Cohomology of vector bundles and syzygies / |
| title_full | Cohomology of vector bundles and syzygies / Jerzy Weyman. |
| title_fullStr | Cohomology of vector bundles and syzygies / Jerzy Weyman. |
| title_full_unstemmed | Cohomology of vector bundles and syzygies / Jerzy Weyman. |
| title_short | Cohomology of vector bundles and syzygies / |
| title_sort | cohomology of vector bundles and syzygies |
| topic | Syzygies (Mathematics) http://id.loc.gov/authorities/subjects/sh85131751 Vector bundles. http://id.loc.gov/authorities/subjects/sh85142450 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Syzygies (Mathématiques) Fibrés vectoriels. Homologie. MATHEMATICS Algebra Linear. bisacsh Homology theory. cct Syzygies (Mathematics) cct Vector bundles. cct Homology theory fast Syzygies (Mathematics) fast Vector bundles fast Syzygie gnd http://d-nb.info/gnd/4326483-9 Kommutative Algebra gnd http://d-nb.info/gnd/4164821-3 Vektorraumbündel gnd http://d-nb.info/gnd/4187470-5 Kohomologietheorie gnd http://d-nb.info/gnd/4164610-1 |
| topic_facet | Syzygies (Mathematics) Vector bundles. Homology theory. Syzygies (Mathématiques) Fibrés vectoriels. Homologie. MATHEMATICS Algebra Linear. Homology theory Vector bundles Syzygie Kommutative Algebra Vektorraumbündel Kohomologietheorie Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=120694 |
| work_keys_str_mv | AT weymanjerzy cohomologyofvectorbundlesandsyzygies |