Algebraic geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2006
|
| Ausgabe: | [Nachdr.] |
| Schriftenreihe: | Graduate texts in mathematics
52 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XVI, 496 S. graph. Darst. |
| ISBN: | 3540902449 9780387902449 |
Internformat
MARC
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| 300 | |a XVI, 496 S. |b graph. Darst. | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 52 | |
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Datensatz im Suchindex
| _version_ | 1804137911606575105 |
|---|---|
| adam_text | Contents
Introduction
xiii
CHAPTER I
Varieties
1
1
Affine
Varieties
1
2
Projective Varieties
8
3
Morphisms
14
4
Rational Maps
24
5
Nonsingular Varieties
31
6
Nonsingular Curves
39
7
Intersections in Projective Space
47
8
What Is Algebraic Geometry?
55
CHAPTER II
Schemes
60
1
Sheaves
60
2
Schemes
69
3
First Properties of Schemes
82
4
Separated and Proper Morphisms
95
5
Sheaves of Modules
108
6
Divisors
129
7
Projective Morphisms
149
8
Differentials
172
9
Formal Schemes
190
CHAPTER HI
Cohomology
201
1
Derived Functors
202
2
Cohomology of Sheaves
206
3
Cohomology of a Noetherian
Affine
Scheme
213
ix
Contents
4
Cech Cohomology
218
5 The Cohomology
of
Projective
Space
225
6
Ext
Groups and Sheaves
233
7
The
Serre
Duality Theorem
239
8
Higher Direct Images of Sheaves
250
9
Flat Morphisms
253
10
Smooth Morphisms
268
1
1
The Theorem on Formal Functions
276
12
The Semicontinuity Theorem
281
CHAPTER IV
Curves
293
1
Riemann-Roch Theorem
294
2
Hurwitz s Theorem
299
3
Embeddings in
Projective
Space
307
4
Elliptic Curves
316
5
The Canonical Embedding
340
6
Classification of Curves in P:!
349
CHAPTER V
Surfaces
356
1
Geometry on a Surface
357
2
Ruled Surfaces
369
3
Monoidal Transformations
386
4
The Cubic Surface in P:!
395
5 Birational
Transformations
409
6
Classification of Surfaces
421
APPENDIX A
Intersection Theory
424
1
Intersection Theory
425
2
Properties of the Chow Ring
428
3
Chern Classes
429
4
The Riemann-Roch Theorem
431
5
Complements and Generalizations
434
APPENDIX
В
Transcendental Methods
438
1
The Associated Complex Analytic Space
438
2
Comparison of the Algebraic and Analytic Categories
440
3
When is a Compact Complex Manifold Algebraic?
441
4 Kahler
Manifolds
445
5
The Exponential Sequence
446
Contents
APPENDIX
С
The Weil
Conjectures
449
1 The
Zeta
Function and the Weil Conjectures
449
2
History of Work on the Weil Conjectures
451
3
The
/-adic Cohomology
453
4
Cohomological Interpretation of the Weil Conjectures
454
Bibliography
459
Results from Algebra
470
Glossary of Notations
472
Index
478
Xl
|
| adam_txt |
Contents
Introduction
xiii
CHAPTER I
Varieties
1
1
Affine
Varieties
1
2
Projective Varieties
8
3
Morphisms
14
4
Rational Maps
24
5
Nonsingular Varieties
31
6
Nonsingular Curves
39
7
Intersections in Projective Space
47
8
What Is Algebraic Geometry?
55
CHAPTER II
Schemes
60
1
Sheaves
60
2
Schemes
69
3
First Properties of Schemes
82
4
Separated and Proper Morphisms
95
5
Sheaves of Modules
108
6
Divisors
129
7
Projective Morphisms
149
8
Differentials
172
9
Formal Schemes
190
CHAPTER HI
Cohomology
201
1
Derived Functors
202
2
Cohomology of Sheaves
206
3
Cohomology of a Noetherian
Affine
Scheme
213
ix
Contents
4
Cech Cohomology
218
5 The Cohomology
of
Projective
Space
225
6
Ext
Groups and Sheaves
233
7
The
Serre
Duality Theorem
239
8
Higher Direct Images of Sheaves
250
9
Flat Morphisms
253
10
Smooth Morphisms
268
1
1
The Theorem on Formal Functions
276
12
The Semicontinuity Theorem
281
CHAPTER IV
Curves
293
1
Riemann-Roch Theorem
294
2
Hurwitz's Theorem
299
3
Embeddings in
Projective
Space
307
4
Elliptic Curves
316
5
The Canonical Embedding
340
6
Classification of Curves in P:!
349
CHAPTER V
Surfaces
356
1
Geometry on a Surface
357
2
Ruled Surfaces
369
3
Monoidal Transformations
386
4
The Cubic Surface in P:!
395
5 Birational
Transformations
409
6
Classification of Surfaces
421
APPENDIX A
Intersection Theory
424
1
Intersection Theory
425
2
Properties of the Chow Ring
428
3
Chern Classes
429
4
The Riemann-Roch Theorem
431
5
Complements and Generalizations
434
APPENDIX
В
Transcendental Methods
438
1
The Associated Complex Analytic Space
438
2
Comparison of the Algebraic and Analytic Categories
440
3
When is a Compact Complex Manifold Algebraic?
441
4 Kahler
Manifolds
445
5
The Exponential Sequence
446
Contents
APPENDIX
С
The Weil
Conjectures
449
1 The
Zeta
Function and the Weil Conjectures
449
2
History of Work on the Weil Conjectures
451
3
The
/-adic Cohomology
453
4
Cohomological Interpretation of the Weil Conjectures
454
Bibliography
459
Results from Algebra
470
Glossary of Notations
472
Index
478
Xl |
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| id | DE-604.BV023484298 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:38:59Z |
| indexdate | 2024-07-09T21:19:49Z |
| institution | BVB |
| isbn | 3540902449 9780387902449 |
| language | English |
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| physical | XVI, 496 S. graph. Darst. |
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| spelling | Hartshorne, Robin 1938- Verfasser (DE-588)133225089 aut Algebraic geometry Robin Hartshorne [Nachdr.] New York [u.a.] Springer 2006 XVI, 496 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 52 Hier auch später erschienene, unveränderte Nachdrucke Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1974 Arcata Calif. gnd-content 2\p (DE-588)4151278-9 Einführung gnd-content 3\p (DE-588)1071861417 Konferenzschrift gnd-content Algebraische Geometrie (DE-588)4001161-6 s DE-604 Graduate texts in mathematics 52 (DE-604)BV000000067 52 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016666373&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hartshorne, Robin 1938- Algebraic geometry Graduate texts in mathematics Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)1071861417 (DE-588)4151278-9 |
| title | Algebraic geometry |
| title_auth | Algebraic geometry |
| title_exact_search | Algebraic geometry |
| title_exact_search_txtP | Algebraic geometry |
| title_full | Algebraic geometry Robin Hartshorne |
| title_fullStr | Algebraic geometry Robin Hartshorne |
| title_full_unstemmed | Algebraic geometry Robin Hartshorne |
| title_short | Algebraic geometry |
| title_sort | algebraic geometry |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraische Geometrie Konferenzschrift 1974 Arcata Calif. Einführung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016666373&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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