书籍详情
代数几何
作者：（美）Robin Hartshorne著
出版社：世界图书出版公司北京公司
出版时间：1999-11-01
ISBN：9787506200820
定价：¥82.00
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内容简介
This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology. The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I， to establish a number of basic concepts and examples. Then the methods of schemes and cohomology are developed in Chapters II and III， with emphasis on applications rather than excessive generality. The last two chapters of the book （IV and V） use these methods to study topics in the classical theory of algebraic curves and surfaces.本书为英文版。
作者简介
暂缺《代数几何》作者简介
目录
Introduction
CHAPTER I
Varieties
1 Affine Varieties
2 Projective Varieties
3 Morphisms
4 Rational Maps
5 Nonsingular Varieties
6 Nonsingular Curves
7 Intersections in Projective Space
8 What Is Algebraic Geometry
CHAPTER II
Schemes
1 Sheaves
2 Schemes
3 First Properties of Schemes
4 Separated and Proper Morphisms
5 Sheaves of Modules
6 Divisors
7 Projective Morphisms
8 Differentials
9 Formal Schemes
CHAPTER III
Cohomology
1 Derived Functors
2 Cohomology of Sheaves
3 Cohomology of a Noetherian Affine Scheme
4 Cech Cohomology
5 The Cohomology of Projective Space
6 Ext Groups and Sheaves
7 The Serre Duality Theorem
8 Higher Direct images of Sheaves
9 Flat Morphisms
10 Smooth Morphisms
11 The Theorem on Formal Functions
12 The Semicontinuity Theorem
CHAPTER IV
Curves
1 Riemann-Roch Theorem
2 Hurwitz''s Theorem
3 Embeddings in Projective Space
4 Elliptic Carves
5 The Canonical Embedding
6 Classification of Curves in P3
CHAPTER V
Surfaces
1 Geometry on a Surface
2 Ruled Surfaces
3 Monoidal Transformations
4 The Cubic Surface in P3
5 Birational Transformations
6 Classification of Surfaces
APPENDIX A
Intersection Theory
1 Intersection Theory
2 Properties of the Chow Ring
3 Chern Classes
4 The Riemann-Roch Theorem
5 Complements and Generalizations
APPENDIX B
Transcendental Methods
1 The Associated Complex Analytic Space
2 Comparison of the Algebraic and Analytic Categories
3 When is a Compact Complex Manifold Algebraic
4 Kahler Manifolds
5 The Exponential Sequence
APPENDIX C
The Weil Conjectures
1 The Zeta Function and the Well Conjectures
2 History of Work on the Weil Conjectures
3 The I-adic Cohomology
4 Cohomological Interpretation of the Well Conjectures
Bibliography
Results from Algebra
Glossary of Notations
Index
CHAPTER I
Varieties
1 Affine Varieties
2 Projective Varieties
3 Morphisms
4 Rational Maps
5 Nonsingular Varieties
6 Nonsingular Curves
7 Intersections in Projective Space
8 What Is Algebraic Geometry
CHAPTER II
Schemes
1 Sheaves
2 Schemes
3 First Properties of Schemes
4 Separated and Proper Morphisms
5 Sheaves of Modules
6 Divisors
7 Projective Morphisms
8 Differentials
9 Formal Schemes
CHAPTER III
Cohomology
1 Derived Functors
2 Cohomology of Sheaves
3 Cohomology of a Noetherian Affine Scheme
4 Cech Cohomology
5 The Cohomology of Projective Space
6 Ext Groups and Sheaves
7 The Serre Duality Theorem
8 Higher Direct images of Sheaves
9 Flat Morphisms
10 Smooth Morphisms
11 The Theorem on Formal Functions
12 The Semicontinuity Theorem
CHAPTER IV
Curves
1 Riemann-Roch Theorem
2 Hurwitz''s Theorem
3 Embeddings in Projective Space
4 Elliptic Carves
5 The Canonical Embedding
6 Classification of Curves in P3
CHAPTER V
Surfaces
1 Geometry on a Surface
2 Ruled Surfaces
3 Monoidal Transformations
4 The Cubic Surface in P3
5 Birational Transformations
6 Classification of Surfaces
APPENDIX A
Intersection Theory
1 Intersection Theory
2 Properties of the Chow Ring
3 Chern Classes
4 The Riemann-Roch Theorem
5 Complements and Generalizations
APPENDIX B
Transcendental Methods
1 The Associated Complex Analytic Space
2 Comparison of the Algebraic and Analytic Categories
3 When is a Compact Complex Manifold Algebraic
4 Kahler Manifolds
5 The Exponential Sequence
APPENDIX C
The Weil Conjectures
1 The Zeta Function and the Well Conjectures
2 History of Work on the Weil Conjectures
3 The I-adic Cohomology
4 Cohomological Interpretation of the Well Conjectures
Bibliography
Results from Algebra
Glossary of Notations
Index
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