The geometry of Syzygies: a second course in commutative algebra and algebraic geometry
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2005
|
| Schriftenreihe: | Graduate Texts in Mathematics
229 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 243 S. Ill., graph. Darst. |
| ISBN: | 0387222154 0387222324 |
Internformat
MARC
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| 100 | 1 | |a Eisenbud, David |d 1947- |e Verfasser |0 (DE-588)139999671 |4 aut | |
| 245 | 1 | 0 | |a The geometry of Syzygies |b a second course in commutative algebra and algebraic geometry |c David Eisenbud |
| 264 | 1 | |a New York, NY |b Springer |c 2005 | |
| 300 | |a XVI, 243 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate Texts in Mathematics |v 229 | |
| 650 | 4 | |a Algebraische Geometrie - Syzygie | |
| 650 | 4 | |a Commutative algebra | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Syzygies (Mathematics) | |
| 650 | 0 | 7 | |a Syzygie |0 (DE-588)4326483-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Syzygie |0 (DE-588)4326483-9 |D s |
| 689 | 0 | 1 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 2 | |a Kommutative Algebra |0 (DE-588)4164821-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Graduate Texts in Mathematics |v 229 |w (DE-604)BV000000067 |9 229 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-012900391 | ||
Datensatz im Suchindex
| _version_ | 1804132912579215360 |
|---|---|
| adam_text | Contents
Preface:
Algebra
and Geometry
ix
What Are Syzygies?
.............................
χ
The Geometric Content of Syzygies
.................... xi
What Does Solving Linear Equations Mean?
.............. . xii
Experiment and Computation
....................... xiii
What s In This Book?
............................ xiv
Prerequisites
................................. xv
How Did This Book Come About?
..................... xv
Other Books
................................. xvi
Thanks
.................................... xvi
Notation
................................... xvi
Free Resolutions and Hubert Functions
1
The Generation of Invariants
........................ 1
Enter Hubert
................................. 2
1A The Study of Syzygies
............................ 3
The Hubert Function Becomes Polynomial
................ 4
IB Minimal Free Resolutions
.......................... 5
Describing Resolutions:
Betti
Diagrams
.................. 7
Properties of the Graded
Betti
Numbers
................. 8
The Information in the Hubert Function
................. 9
1С
Exercises
................................... 10
First Examples of Free Resolutions
15
2
A Monomial Ideals and Simplicial Complexes
................ 15
Simplicial Complexes
............................ 15
Labeling by Monomials
........................... 16
Syzygies of Monomial Ideals
........................ 18
2В
Bounds on
Betti
Numbers and Proof of Hubert s Syzygy Theorem
... 20
2C Geometry from Syzygies: Seven Points in P3
............... 22
The Hubert Polynomial and Function
.................... 23
...
and Other Information in the Resolution
................ 24
2D Exercises
................................... 27
3
Points in P2
31
ЗА
The Ideal of a Finite Set of Points
..................... 32
3B Examples
................................... 39
3C Existence of Sets of Points with Given Invariants
............. 42
3D
Exercises
................................... 47
4
Castelnuovo—Mumford Regularity
55
4A Definition and First Applications
...................... 55
4B Characterizations of Regularity: Cohomology
............... 58
4C The Regularity of a Cohen-Macaulay Module
............. . 65
4D The Regularity of a Coherent Sheaf
................... . 67
4E Exercises
................................... 68
5
The Regularity of
Projective
Curves
73
5A A General Regularity Conjecture
...................... 73
5B Proof of the Gruson-Lazarsfeld-Peskine Theorem
............ 75
5C Exercises
................................... 85
6
Linear Series and l-Generic Matrices
89
6A Rational Normal Curves
........................... 90
6A.1 Where d That Matrix Come From?
................. 91
6B l-Generic Matrices
.............................. 92
6C Linear Series
................................. 95
6D Elliptic Normal Curves
........................... 103
6E Exercises
................................... 113
7
Linear Complexes and the Linear Syzygy Theorem
119
7A Linear Syzygies
............................... 120
7B The Bernstein-Gelfand-Gelfand Correspondence
............. 124
7C Exterior Minors and Annihilators
..................... 130
7D Proof of the Linear Syzygy Theorem
.................... 135
7E More about the Exterior Algebra and BGG
................ 136
7F Exercises
................................... 143
8
Curves of High Degree
145
8A The Cohen-Macaulay Property
....................... 146
8A.1 The Restricted Tautological Bundle
................ 148
8B Strands of the Resolution
.......................... 153
8B.1 The Cubic Strand
.......................... 155
8B.2 The Quadratic Strand
........................ 159
8C Conjectures and Problems
......................... 169
8D Exercises
................................... 171
9
Clifford Index and Canonical Embedding
177
9A The Cohen-Macaulay Property and the Clifford Index
..........177
9B Green s Conjecture
.............................180
9C Exercises
...................................185
Appendix
1
Introduction to Local Cohomology
187
AIA
Definitions and Tools
............................187
A1B Local Cohomology and Sheaf Cohomology
................195
A
1С
Vanishing and Nonvanishing Theorems
..................198
AID Exercises
.................................. . 199
Appendix
2
A Jog Through Commutative Algebra
201
A2A Associated Primes and Primary Decomposition
.............. 202
A2B Dimension and Depth
............................ 205
A2C
Projective
Dimension and Regular Local Rings
.............. 208
A2D Normalization: Resolution of Singularities for Curves
.......... 210
A2E The Cohen-Macaulay Property
....................... 213
A2F The
Koszul
Complex
............................ 217
A2G Fitting Ideals and Other Determinantal Ideals
.............. 220
A2H The Eagon-Northcott Complex and Scrolls
................ 222
References
227
Index
237
|
| any_adam_object | 1 |
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| 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 | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019522296 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:00:22Z |
| institution | BVB |
| isbn | 0387222154 0387222324 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012900391 |
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| physical | XVI, 243 S. Ill., graph. Darst. |
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| spelling | Eisenbud, David 1947- Verfasser (DE-588)139999671 aut The geometry of Syzygies a second course in commutative algebra and algebraic geometry David Eisenbud New York, NY Springer 2005 XVI, 243 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate Texts in Mathematics 229 Algebraische Geometrie - Syzygie Commutative algebra Geometry, Algebraic Syzygies (Mathematics) Syzygie (DE-588)4326483-9 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Syzygie (DE-588)4326483-9 s Algebraische Geometrie (DE-588)4001161-6 s Kommutative Algebra (DE-588)4164821-3 s DE-604 Graduate Texts in Mathematics 229 (DE-604)BV000000067 229 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012900391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eisenbud, David 1947- The geometry of Syzygies a second course in commutative algebra and algebraic geometry Graduate Texts in Mathematics Algebraische Geometrie - Syzygie Commutative algebra Geometry, Algebraic Syzygies (Mathematics) Syzygie (DE-588)4326483-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4326483-9 (DE-588)4001161-6 (DE-588)4164821-3 |
| title | The geometry of Syzygies a second course in commutative algebra and algebraic geometry |
| title_auth | The geometry of Syzygies a second course in commutative algebra and algebraic geometry |
| title_exact_search | The geometry of Syzygies a second course in commutative algebra and algebraic geometry |
| title_full | The geometry of Syzygies a second course in commutative algebra and algebraic geometry David Eisenbud |
| title_fullStr | The geometry of Syzygies a second course in commutative algebra and algebraic geometry David Eisenbud |
| title_full_unstemmed | The geometry of Syzygies a second course in commutative algebra and algebraic geometry David Eisenbud |
| title_short | The geometry of Syzygies |
| title_sort | the geometry of syzygies a second course in commutative algebra and algebraic geometry |
| title_sub | a second course in commutative algebra and algebraic geometry |
| topic | Algebraische Geometrie - Syzygie Commutative algebra Geometry, Algebraic Syzygies (Mathematics) Syzygie (DE-588)4326483-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Algebraische Geometrie - Syzygie Commutative algebra Geometry, Algebraic Syzygies (Mathematics) Syzygie Algebraische Geometrie Kommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012900391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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