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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
2003
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| Schriftenreihe: | Cambridge tracts in mathematics
149 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 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-Ressource (xiv, 371 Seiten) |
| ISBN: | 9780511546556 |
| DOI: | 10.1017/CBO9780511546556 |
Internformat
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| 100 | 1 | |a Weyman, Jerzy |d 1955- |e Verfasser |0 (DE-588)172463521 |4 aut | |
| 245 | 1 | 0 | |a Cohomology of vector bundles and syzygies |c Jerzy Weyman |
| 246 | 1 | 3 | |a Cohomology of Vector Bundles & Syzygies |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2003 | |
| 300 | |a 1 Online-Ressource (xiv, 371 Seiten) | ||
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| 490 | 0 | |a Cambridge tracts in mathematics |v 149 | |
| 505 | 8 | 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 | ||
| 650 | 4 | |a Syzygies (Mathematics) | |
| 650 | 4 | |a Vector bundles | |
| 650 | 4 | |a Homology theory | |
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| 689 | 0 | 1 | |a Vektorraumbündel |0 (DE-588)4187470-5 |D s |
| 689 | 0 | 2 | |a Homologietheorie |0 (DE-588)4141714-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804176883689979904 |
|---|---|
| any_adam_object | |
| author | Weyman, Jerzy 1955- |
| author_GND | (DE-588)172463521 |
| author_facet | Weyman, Jerzy 1955- |
| author_role | aut |
| author_sort | Weyman, Jerzy 1955- |
| author_variant | j w jw |
| building | Verbundindex |
| bvnumber | BV043941652 |
| classification_rvk | SK 240 SK 350 SK 320 |
| collection | ZDB-20-CBO |
| 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 | (ZDB-20-CBO)CR9780511546556 (OCoLC)850267633 (DE-599)BVBBV043941652 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511546556 |
| format | Electronic eBook |
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| id | DE-604.BV043941652 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511546556 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350622 |
| oclc_num | 850267633 |
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| physical | 1 Online-Ressource (xiv, 371 Seiten) |
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| publishDate | 2003 |
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| publisher | Cambridge University Press |
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| spelling | Weyman, Jerzy 1955- Verfasser (DE-588)172463521 aut Cohomology of vector bundles and syzygies Jerzy Weyman Cohomology of Vector Bundles & Syzygies Cambridge Cambridge University Press 2003 1 Online-Ressource (xiv, 371 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 149 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 Syzygies (Mathematics) Vector bundles Homology theory Vektorraumbündel (DE-588)4187470-5 gnd rswk-swf Syzygie (DE-588)4326483-9 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 Erscheint auch als Druck-Ausgabe 978-0-521-62197-7 https://doi.org/10.1017/CBO9780511546556 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Weyman, Jerzy 1955- Cohomology of vector bundles and syzygies 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) Vector bundles Homology theory Vektorraumbündel (DE-588)4187470-5 gnd Syzygie (DE-588)4326483-9 gnd Homologietheorie (DE-588)4141714-8 gnd |
| subject_GND | (DE-588)4187470-5 (DE-588)4326483-9 (DE-588)4141714-8 |
| title | Cohomology of vector bundles and syzygies |
| title_alt | Cohomology of Vector Bundles & Syzygies 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) Vector bundles Homology theory Vektorraumbündel (DE-588)4187470-5 gnd Syzygie (DE-588)4326483-9 gnd Homologietheorie (DE-588)4141714-8 gnd |
| topic_facet | Syzygies (Mathematics) Vector bundles Homology theory Vektorraumbündel Syzygie Homologietheorie |
| url | https://doi.org/10.1017/CBO9780511546556 |
| work_keys_str_mv | AT weymanjerzy cohomologyofvectorbundlesandsyzygies AT weymanjerzy cohomologyofvectorbundlessyzygies |