《代數幾何入門》是2010年世界圖書出版公司出版的圖書。本書旨在深層次講述代數幾何原理、20世紀的一些重要進展和數學實踐中正在探討的問題。
基本介紹
- 書名：代數幾何入門
- ISBN：9787510005152, 7510005159
- 頁數：161
- 出版社：世界圖書出版公司
- 出版時間：第1版 (2010年1月1日)
- 裝幀：平裝
- 開本：24
目錄,
內容簡介
該書的內容對於對代數幾何不是很了解或了解甚少，但又想要了解代數幾何基礎的數學工作者是非常有用的。目次：仿射代數變數；代數基礎；射影變數；Quasi射影變數；經典結構；光滑；雙有理幾何學；映射到射影空間。
讀者對象：《代數幾何入門(英文版)》適用於數學專業高年級本科生、研究生和與該領域有關的工作者。
目錄
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
