Cohomology of vector bundles and syzygies:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
149 |
| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 371 S. |
| ISBN: | 0521621976 9780521621977 |
Staff View
MARC
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| 100 | 1 | |a Weyman, Jerzy |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Cohomology of vector bundles and syzygies |c Jerzy Weyman |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XIV, 371 S. | ||
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| 490 | 1 | |a Cambridge tracts in mathematics |v 149 | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Syzygies (Mathematics) | |
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Record in the Search Index
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| adam_text | Contents
Preface page xi
1 Introductory Material 1
1.1 Multilinear Algebra and Combinatorics 1
1.2 Homological and Commutative Algebra 12
1.3 Determinants of Complexes 27
2 Schur Functors and Schur Complexes 32
2.1 Schur Functors and Weyl Functors 32
2.2 Schur Functors and Highest Weight Theory 49
2.3 Properties of Schur Functors. Cauchy Formulas, Littlewood
Richardson Rule, and Plethysm 57
2.4 The Schur Complexes 66
Exercises for Chapter 2 78
3 Grassmannians and Flag Varieties 85
3.1 The Plucker Embeddings 85
3.2 The Standard Open Coverings of Flag Manifolds
and the Straightening Law 91
3.3 The Homogeneous Vector Bundles on Flag Manifolds 98
Exercises for Chapter 3 104
4 Bott s Theorem 110
4.1 The Formulation of Bott s Theorem for the General
Linear Group 110
4.2 The Proof of Bott s Theorem for the General
Linear Group 117
4.3 Bott s Theorem for General Reductive Groups 123
Exercises for Chapter 4 132
5 The Geometric Technique 136
5.1 The Formulation of the Basic Theorem 137
5.2 The Proof of the Basic Theorem 141
5.3 The Proof of Properties of Complexes F(V). 146
ix
x Contents
5.4 The G Equivariant Setup 149
5.5 The Differentials in Complexes F(V).. 152
5.6 Degeneration Sequences 154
Exercises for Chapter 5 156
6 The Determinantal Varieties 159
6.1 The Lascoux Resolution 160
6.2 The Resolutions of Determinantal Ideals
in Positive Characteristic 168
6.3 The Determinantal Ideals for Symmetric Matrices 175
6.4 The Determinantal Ideals for Skew Symmetric Matrices 187
6.5 Modules Supported in Determinantal Varieties 195
6.6 Modules Supported in Symmetric
Determinantal Varieties 209
6.7 Modules Supported in Skew Symmetric
Determinantal Varieties 213
Exercises for Chapter 6 218
7 Higher Rank Varieties 228
7.1 Basic Properties 228
7.2 Rank Varieties for Symmetric Tensors 234
7.3 Rank Varieties for Skew Symmetric Tensors 239
Exercises for Chapter 7 245
8 The Nilpotent Orbit Closures 251
8.1 The Closures of Conjugacy Classes of Nilpotent Matrices 252
8.2 The Equations of the Conjugacy Classes
of Nilpotent Matrices 263
8.3 The Nilpotent Orbits for Other Simple Groups 278
8.4 Conjugacy Classes for the Orthogonal Group 283
8.5 Conjugacy Classes for the Symplectic Group 296
Exercises for Chapter 8 309
9 Resultants and Discriminants 313
9.1 The Generalized Resultants 314
9.2 The Resultants of Multihomogeneous Polynomials 318
9.3 The Generalized Discriminants 328
9.4 The Hyperdeterminants 332
Exercises for Chapter 9 355
References 359
Notation Index 367
Subject Index 369
|
| any_adam_object | 1 |
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| indexdate | 2024-07-09T19:04:34Z |
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| isbn | 0521621976 9780521621977 |
| language | English |
| lccn | 2002074071 |
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| series2 | Cambridge tracts in mathematics |
| spelling | Weyman, Jerzy Verfasser aut Cohomology of vector bundles and syzygies Jerzy Weyman 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2003 XIV, 371 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 149 Includes bibliographical references and index Homology theory Syzygies (Mathematics) Vector bundles Syzygie (DE-588)4326483-9 gnd rswk-swf Vektorraumbündel (DE-588)4187470-5 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Syzygie (DE-588)4326483-9 s Vektorraumbündel (DE-588)4187470-5 s Homologietheorie (DE-588)4141714-8 s DE-604 Cambridge tracts in mathematics 149 (DE-604)BV000000001 149 http://www.loc.gov/catdir/description/cam031/2002074071.html Publisher description http://www.loc.gov/catdir/toc/cam031/2002074071.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940616&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weyman, Jerzy Cohomology of vector bundles and syzygies Cambridge tracts in mathematics Homology theory Syzygies (Mathematics) Vector bundles Syzygie (DE-588)4326483-9 gnd Vektorraumbündel (DE-588)4187470-5 gnd Homologietheorie (DE-588)4141714-8 gnd |
| subject_GND | (DE-588)4326483-9 (DE-588)4187470-5 (DE-588)4141714-8 |
| title | Cohomology of vector bundles and syzygies |
| 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 | Homology theory Syzygies (Mathematics) Vector bundles Syzygie (DE-588)4326483-9 gnd Vektorraumbündel (DE-588)4187470-5 gnd Homologietheorie (DE-588)4141714-8 gnd |
| topic_facet | Homology theory Syzygies (Mathematics) Vector bundles Syzygie Vektorraumbündel Homologietheorie |
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| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT weymanjerzy cohomologyofvectorbundlesandsyzygies |