Determinantal rings:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1988
|
| Schriftenreihe: | Lecture notes in mathematics
1327 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Weitere Ausgabe: Monografias de matemática ; 45 |
| Beschreibung: | VII, 236 S. |
| ISBN: | 3540194681 0387194681 |
Internformat
MARC
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| 245 | 1 | 0 | |a Determinantal rings |c Winfried Bruns ; Udo Vetter |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1988 | |
| 300 | |a VII, 236 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1327 | |
| 500 | |a Weitere Ausgabe: Monografias de matemática ; 45 | ||
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Datensatz im Suchindex
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| adam_text | Contents
1. Preliminaries 1
A. Notations and Conventions 1
B. Minors and Determinantal Ideals 3
C. Determinantal Rings and Varieties 4
D. Schubert Varieties and Schubert Cycles 6
E. Comments and References 9
2. Ideals of Maximal Minors 10
A. Classical Results on Height and Grade 10
B. The Perfection of Im(X) and Some Consequences 13
C. The Eagon Northcott Complex 16
D. The Complex of Gulliksen and Negard 22
E. Comments and References 25
3. Generically Perfect Ideals 27
A. The Transfer of Perfection 27
B. The Substitution of Indeterminates by a Regular Sequence 30
C. The Transfer of Integrity and Related Properties 34
D. The Bound for the Height of Specializations 36
E. Comments and References 36
4. Algebras with Straightening Law on Posets of Minors 38
A. Algebras with Straightening Law 38
B. G(X) as an ASL 40
C. The Linear Independence of the Standard Monomials in G(X) .... 43
D. B[X] as an ASL 45
E. Comments and References 48
5. The Structure of an ASL 50
A. ASL Structures on Residue Class Rings 50
B. Syzygies and the Straightening Law 53
C. Nilpotents, Regular Elements and Dimension 54
D. Wonderful Posets and the Cohen Macaulay Property 58
E. The Arithmetical Rank of Certain Ideals 61
F. Comments and References 63
6. Integrity and Normality. The Singular Locus 64
A. Integrity and Normality 64
B. The Singular Locus 67
C. Comments and References 72
vi Contents
7. Generic Points and Invariant Theory 73
A. A Generic Point for Rr+J (X) 73
B. Invariants and Absolute Invariants 74
C. The Main Theorem of Invariant Theory for GL and SL 76
D. Remarks on Invariant Theory 80
E. The Classical Generic Point for G(X; 7) 82
F. G(X; 7) and R(X;6) as Rings of Invariants 84
G. The Depth of Modules of Invariants 88
H. Comments and References 91
8. The Divisor Class Group and the Canonical Class 93
A. The Divisor Class Group 93
B. The Canonical Class of Rr+i(X) 97
C. The General Case 100
D. Comments and References 104
9. Powers of Ideals of Maximal Minors 105
A. Ideals and Subalgebras of Maximal Minors 105
B. ASL Structures on Graded Algebras Derived from an Ideal 108
C. Graded Algebras with Respect to Ideals of Maximal Minors . . . • 112
D. The Depth of Powers of Ideals of Maximal Minors 117
E. Comments and References 120
10. Primary Decomposition 122
A. Symbolic Powers of Determinantal Ideals 122
B. The Symbolic Graded Ring 124
C. Primary Decomposition of Products of Determinantal Ideals .... 126
D. Comments and References 123
11. Representation Theory 135
A. The Filtration of K[X] by the Intersections of Symbolic Powers ... 135
B. Bitableaux and the Straightening Law Revisited 137
C. The Decomposition of K[X] into Irreducible G Submodules .... 141
D. G Invariant Ideals 145
E. [/ Invariants and Algebras Generated by Minors 149
F. Comments and References 152
12. Principal Radical Systems 15S
A. A Propedeutic Example. Principal Radical Systems • l5^
B. A Principal Radical System for the Determinantal Ideals I55
C. The Perfection of Determinantal Ideals 158
D. Comments and References 160
18. Generic Modules 162
A. The Perfection of the Image of a Generic Map 162
B. The Perfection of a Generic Module 165
C. Homological Properties of Generic Modules 171
D. Comments and References 173
Contents vii
14. The Module of Kahler Differentials 174
A. Perfection and Syzygies of Some Determinantal Ideals 175
B. The Lower Bound for the Depth of the Differential Module 177
C. The Syzygetic Behaviour of the Differential Module 181
D. Comments and References 183
15. Derivations and Rigidity 184
A. The Lower Bound for the Depth of the Module of Derivations .... 184
B. The Perfection of the Module of Derivations 189
C. Syzygetic Behaviour and Rigidity 197
D. Comments and References 201
16. Appendix 202
A. Determinants and Modules. Rank 202
B. Grade and Acyclicity 206
C. Perfection and the Cohen Macaulay Property 209
D. Dehomogenization 211
E. How to Compare Torsionfree 213
F. The Theorem of Hilbert Burch 217
G. Comments and References 218
Bibliography 219
Index of Notations 229
Subject Index 232
|
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| classification_tum | MAT 160f |
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| discipline | Mathematik |
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| id | DE-604.BV000858961 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:20:37Z |
| institution | BVB |
| isbn | 3540194681 0387194681 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000539214 |
| oclc_num | 230937305 |
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| physical | VII, 236 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bruns, Winfried Verfasser aut Determinantal rings Winfried Bruns ; Udo Vetter Berlin [u.a.] Springer 1988 VII, 236 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1327 Weitere Ausgabe: Monografias de matemática ; 45 Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Determinantenring (DE-588)4201236-3 gnd rswk-swf Determinantenring (DE-588)4201236-3 s DE-604 Kommutative Algebra (DE-588)4164821-3 s Vetter, Udo Verfasser aut Lecture notes in mathematics 1327 (DE-604)BV000676446 1327 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000539214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bruns, Winfried Vetter, Udo Determinantal rings Lecture notes in mathematics Kommutative Algebra (DE-588)4164821-3 gnd Determinantenring (DE-588)4201236-3 gnd |
| subject_GND | (DE-588)4164821-3 (DE-588)4201236-3 |
| title | Determinantal rings |
| title_auth | Determinantal rings |
| title_exact_search | Determinantal rings |
| title_full | Determinantal rings Winfried Bruns ; Udo Vetter |
| title_fullStr | Determinantal rings Winfried Bruns ; Udo Vetter |
| title_full_unstemmed | Determinantal rings Winfried Bruns ; Udo Vetter |
| title_short | Determinantal rings |
| title_sort | determinantal rings |
| topic | Kommutative Algebra (DE-588)4164821-3 gnd Determinantenring (DE-588)4201236-3 gnd |
| topic_facet | Kommutative Algebra Determinantenring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000539214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT brunswinfried determinantalrings AT vetterudo determinantalrings |