Power sums, Gorenstein algebras, and determinantal loci:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Schriftenreihe: | Lecture notes in mathematics
1721 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXXI, 345 S. Ill. |
| ISBN: | 3540667660 |
Internformat
MARC
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| 100 | 1 | |a Iarrobino, Anthony A. |d 1943- |e Verfasser |0 (DE-588)12149246X |4 aut | |
| 245 | 1 | 0 | |a Power sums, Gorenstein algebras, and determinantal loci |c Anthony Iarrobino ; Vassil Kanev |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XXXI, 345 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1721 | |
| 650 | 7 | |a Algebra comutativa |2 larpcal | |
| 650 | 7 | |a Geometria algebrica |2 larpcal | |
| 650 | 4 | |a Hilbert, Schémas de | |
| 650 | 4 | |a Matrices catalectiques | |
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
| 650 | 4 | |a Variétés déterminantielles | |
| 650 | 4 | |a Catalecticant matrices | |
| 650 | 4 | |a Determinantal varieties | |
| 650 | 4 | |a Hilbert schemes | |
| 650 | 0 | 7 | |a Gorenstein-Ring |0 (DE-588)4157921-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Potenzreihe |0 (DE-588)4138577-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Determinantenvarietät |0 (DE-588)4582676-6 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kanev, Vassil I. |d 1954- |e Verfasser |0 (DE-588)121492540 |4 aut | |
| 700 | 1 | 2 | |a Iarrobino, Anthony A. |d 1943- |0 (DE-588)12149246X |4 aut |t The Gotzmann theorems and the Hilbert scheme |
| 700 | 1 | 2 | |a Kleiman, Steven L. |d 1942- |0 (DE-588)120837994 |4 aut |t The Gotzmann theorems and the Hilbert scheme |
| 830 | 0 | |a Lecture notes in mathematics |v 1721 |w (DE-604)BV000676446 |9 1721 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008736233 | ||
| 249 | |a <<With an appendix The>> Gotzmann theorems and the Hilbert scheme |v by Anthony Iarrobino and Steven L. Kleiman | ||
Datensatz im Suchindex
| _version_ | 1804127518248140800 |
|---|---|
| adam_text | Contents
Introduction: Informal History and Brief Outline xiii
0.1. Canonical forms, and catalecticant matrices of higher
partial derivatives of a form xiii
0.2. Apolarity and Artinian Gorenstein algebras xviii
0.3. Families of sets of points xxi
0.4. Brief summary of chapters xxii
Part I. Catalecticant Varieties 1
Chapter 1. Forms and Catalecticant Matrices 3
1.1. Apolarity and catalecticant varieties: the dimensions of
the vector spaces of higher partials 3
1.2. Determinantal loci of the first catalecticant, the Jacobian 16
1.3. Binary forms and Hankel matrices 22
1.4. Detailed summary and preparatory results 41
Chapter 2. Sums of Powers of Linear Forms, and Gorenstein
Algebras 57
2.1. Waring s problem for general forms 57
2.2. Uniqueness of additive decompositions 62
2.3. The Gorenstein algebra of a homogeneous polynomial 67
Chapter 3. Tangent Spaces to Catalecticant Schemes 73
3.1. The tangent space to the determinantal scheme Vs(u, v; r)
of the catalecticant matrix 73
3.2. The tangent space to the scheme Gor(T) parametrizing
forms with fixed dimensions of the partials 79
Chapter 4. The Locus PS(s,j;r) of Sums of Powers, and
Determinantal Loci of Catalecticant Matrices 91
4.1. Thecaser = 3 92
4.2. Sets of s points in IP7 1 and Gorenstein ideals 102
XII
4.3. Gorenstein ideals whose lowest degree generators are a
complete intersection 108
4.4. The smoothness and dimension of the scheme Gor(T)
when r — 3: a survey 116
Part II. Catalecticant Varieties and the Punctual Hilbert
Scheme 129
Chapter 5. Forms and Zero Dimensional Schemes I: Basic Results,
and the Case r = 3 131
5.1. Annihilating scheme in Fr~l of a form 135
5.2. Flat families of zero dimensional schemes and limit ideals 142
5.3. Existence theorems for annihilating schemes when r = 3 150
5.3.1. The generator and relation strata of the variety Gor(T)
parametrizing Gorenstein algebras 151
5.3.2. The morphism from Gor(T): the case T D (s, s, s) 156
5.3.3. Morphism: the case TD (s — a,s,s,s — a) 167
5.3.4. Morphism: the case T D (s — a,s,s — a) 172
5.3.5. A dimension formula for the variety Gor(T) 179
5.4. Power sum representations in three and more variables 182
5.5. Betti strata of the punctual Hilbert scheme 189
5.6. The length of a form, and the closure of the locus
PS(s, j; 3) of power sums 197
5.7. Codimension three Gorenstein schemes in Pn 201
Chapter 6. Forms and Zero Dimensional Schemes, II: Annihilating
Schemes and Reducible Gor(T) 207
6.1. Uniqueness of the annihilating scheme; closure of
PS(s,j;r) 208
6.2. Varieties Gor(T), T = T(j, r), with several components 214
6.3. Other reducible varieties Gor(T) 224
6.4. Locally Gorenstein annihilating schemes 226
Chapter 7. Connectedness and Components of the Determinantal
Locus FVs(u,v r) 237
7.1. Connectedness of PVs{u,v;r) 237
7.2. The irreducible components of Vs(u,v;r) 241
7.3. Multisecant varieties of the Veronese variety 245
Chapter 8. Closures of the Variety Gor(T), and the Parameter
Space G(T) of Graded Algebras 249
Chapter 9. Questions and Problems 255
XIII
Appendix A. Divided Power Rings and Polynomial Rings 265
Appendix B. Height Three Gorenstein Ideals 271
B.I. Pfaffian formulas 272
B.2. Resolutions of height 3 Gorenstein ideals and their squares 276
B.3. Resolutions of annihilating ideals of power sums 280
B.4. Maximum Betti numbers, given T 282
Appendix C. The Gotzmann Theorems and the Hilbert Scheme
(Anthony Iarrobino and Steven L. Kleiman) 289
C.I. Order sequences and Macaulay s Theorem on Hilbert
functions 290
C.2. Macaulay and Gotzmann polynomials 293
C.3. Gotzmann s Persistence Theorem and m Regularity 297
C.4. The Hilbert scheme HUb^F 1) 302
C.5. Gorenstein sequences having a subsequence of maximal
growth, and Hilbp(Pr 1) 307
Appendix D. Examples of Macaulay Scripts 313
Appendix E. Concordance with the 1996 Version 317
References 319
Index 335
Index of Names 341
Index of Notation 343
|
| any_adam_object | 1 |
| author | Iarrobino, Anthony A. 1943- Kanev, Vassil I. 1954- Iarrobino, Anthony A. 1943- Kleiman, Steven L. 1942- |
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| author_facet | Iarrobino, Anthony A. 1943- Kanev, Vassil I. 1954- Iarrobino, Anthony A. 1943- Kleiman, Steven L. 1942- |
| author_role | aut aut aut aut |
| author_sort | Iarrobino, Anthony A. 1943- |
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| dewey-full | 516.3/5 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 516.3/5 510 |
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| discipline | Mathematik |
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| id | DE-604.BV012839107 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:34:37Z |
| institution | BVB |
| isbn | 3540667660 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008736233 |
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| physical | XXXI, 345 S. Ill. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Iarrobino, Anthony A. 1943- Verfasser (DE-588)12149246X aut Power sums, Gorenstein algebras, and determinantal loci Anthony Iarrobino ; Vassil Kanev Berlin [u.a.] Springer 1999 XXXI, 345 S. Ill. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1721 Algebra comutativa larpcal Geometria algebrica larpcal Hilbert, Schémas de Matrices catalectiques Numerieke wiskunde gtt Variétés déterminantielles Catalecticant matrices Determinantal varieties Hilbert schemes Gorenstein-Ring (DE-588)4157921-5 gnd rswk-swf Potenzreihe (DE-588)4138577-9 gnd rswk-swf Determinantenvarietät (DE-588)4582676-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Potenzreihe (DE-588)4138577-9 s Gorenstein-Ring (DE-588)4157921-5 s Determinantenvarietät (DE-588)4582676-6 s DE-604 Kanev, Vassil I. 1954- Verfasser (DE-588)121492540 aut Iarrobino, Anthony A. 1943- (DE-588)12149246X aut The Gotzmann theorems and the Hilbert scheme Kleiman, Steven L. 1942- (DE-588)120837994 aut The Gotzmann theorems and the Hilbert scheme Lecture notes in mathematics 1721 (DE-604)BV000676446 1721 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008736233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis <<With an appendix The>> Gotzmann theorems and the Hilbert scheme by Anthony Iarrobino and Steven L. Kleiman |
| spellingShingle | Iarrobino, Anthony A. 1943- Kanev, Vassil I. 1954- Iarrobino, Anthony A. 1943- Kleiman, Steven L. 1942- Power sums, Gorenstein algebras, and determinantal loci Lecture notes in mathematics Algebra comutativa larpcal Geometria algebrica larpcal Hilbert, Schémas de Matrices catalectiques Numerieke wiskunde gtt Variétés déterminantielles Catalecticant matrices Determinantal varieties Hilbert schemes Gorenstein-Ring (DE-588)4157921-5 gnd Potenzreihe (DE-588)4138577-9 gnd Determinantenvarietät (DE-588)4582676-6 gnd |
| subject_GND | (DE-588)4157921-5 (DE-588)4138577-9 (DE-588)4582676-6 (DE-588)4113937-9 |
| title | Power sums, Gorenstein algebras, and determinantal loci |
| title_alt | The Gotzmann theorems and the Hilbert scheme |
| title_auth | Power sums, Gorenstein algebras, and determinantal loci |
| title_exact_search | Power sums, Gorenstein algebras, and determinantal loci |
| title_full | Power sums, Gorenstein algebras, and determinantal loci Anthony Iarrobino ; Vassil Kanev |
| title_fullStr | Power sums, Gorenstein algebras, and determinantal loci Anthony Iarrobino ; Vassil Kanev |
| title_full_unstemmed | Power sums, Gorenstein algebras, and determinantal loci Anthony Iarrobino ; Vassil Kanev |
| title_short | Power sums, Gorenstein algebras, and determinantal loci |
| title_sort | power sums gorenstein algebras and determinantal loci |
| topic | Algebra comutativa larpcal Geometria algebrica larpcal Hilbert, Schémas de Matrices catalectiques Numerieke wiskunde gtt Variétés déterminantielles Catalecticant matrices Determinantal varieties Hilbert schemes Gorenstein-Ring (DE-588)4157921-5 gnd Potenzreihe (DE-588)4138577-9 gnd Determinantenvarietät (DE-588)4582676-6 gnd |
| topic_facet | Algebra comutativa Geometria algebrica Hilbert, Schémas de Matrices catalectiques Numerieke wiskunde Variétés déterminantielles Catalecticant matrices Determinantal varieties Hilbert schemes Gorenstein-Ring Potenzreihe Determinantenvarietät Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008736233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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