代数几何入门
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作者： （美）史密斯 著
出 版 社： 世界图书出版公司
出版时间： 2010-1-1字数：版次： 1页数： 160印刷时间： 2010-1-1开本： 24开印次： 1纸张： 胶版纸I S B N ： 9787510005152包装： 平装
本书旨在深层次讲述代数几何原理、20世纪的一些重要进展和数学实践中正在探讨的问题。该书的内容对于对代数几何不是很了解或了解甚少，但又想要了解代数几何基础的数学工作者是非常有用的。目次：仿射代数变量；代数基础；射影变量；Quasi射影变量；经典结构；光滑；双有理几何学；映射到射影空间。
读者对象：本书适用于数学专业高年级本科生、研究生和与该领域有关的工作者。
Notes for the Second Printing
Preface
Acknowledgments
Index of Notation
1 Affine Algebraic Varieties
1.1 Definition and Examples
1.2 The Zariski Topology
1.3 Morphisms of Affine Algebraic Varieties
1.4 Dimension
2 Algebraic Foundations
2.1 A Quick Review of Commutative Ring Theory
2.2 Hilbert's Basis Theorem
2.3 Hilbert's NuUstellensatz
2.4 The Coordinate Ring
2.5 The Equivalence of Algebra and Geometry
2.6 The Spectrum of a Ring
3 Projective Varieties
3.1 Projective Space
3.2 Projective Varieties
3.3 The Projective Closure of an Affine Variety
3.4 Morphisms of Projective Varieties
3.5 Automorphisms of Projective Space
4 Quasi-Projective Varieties
4.1 Quasi-Projective Varieties
4.2 A Basis for the Zariski Topology
4.3 Regular Functions
5 Classical Constructions
5.1 Veronese Maps
5.2 Five Points Determine a Conic
5.3 The Segre Map and Products of Varieties
5.4 Grassmannians
5.5 Degree
5.6 The Hilbert Function
6 Smoothness
6.1 The Tangent Space at a Point
6.2 Smooth Points
6.3 Smoothness in Families
6.4 Bertini's Theorem
6.5 The Gauss Mapping
7 Birational Geometry
7.1 Resolution of Singularities
7.2 Rational Maps
7.3 Birational Equivalence
7.4 Blowing Up Along an Ideal
7.5 Hypersurfaces
7.6 The Classification Problems
8 Maps to Projective Space
8.1 Embedding a Smooth Curve in Three-Space
8.2 Vector Bundles and Line Bundles
8.3 The Sections of a Vector Bundle
8.4 Examples of Vector Bundles
8.5 Line Bundles and Rational Maps
8.6 Very Ample Line Bundles
A Sheaves and Abstract Algebraic Varieties
A.1 Sheaves
A.2 Abstract Algebraic Varieties
References
Index
