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代数几何入门 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- KarenE.Smith，LauriKahanpaa著 著
- 出版社： 世界图书北京出版公司
- ISBN：9787510005152
- 出版时间：2010
- 标注页数：161页
- 文件大小：16MB
- 文件页数：178页
- 主题词：代数几何－英文
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图书目录
1 Affine Algebraic Varieties1
1.1 Definition and Examples2
1.2 The Zariski Topology6
1.3 Morphisms of Affine Algebraic Varieties9
1.4 Dimension11
2 Algebraic Foundations15
2.1 A Quick Review of Commutative Ring Theory15
2.2 Hilbert's Basis Theorem18
2.3 Hilbert's Nullstellensatz20
2.4 The Coordinate Ring23
2.5 The Equivalence of Algebra and Geometry26
2.6 The Spectrum of a Ring30
3 Projective Varieties33
3.1 Projective Space33
3.2 Projective Varieties37
3.3 The Projective Closure of an Affine Variety41
3.4 Morphisms of Projective Varieties44
3.5 Automorphisms of Projective Space47
4 Quasi-Projective Varieties51
4.1 Quasi-Projective Varieties51
4.2 A Basis for the Zariski Topology55
4.3 Regular Functions56
5 Classical Constructions63
5.1 Veronese Maps63
5.2 Five Points Determine a Conic65
5.3 The Segre Map and Products of Varieties67
5.4 Grassmannians71
5.5 Degree74
5.6 The Hilbert Function81
6 Smoothness85
6.1 The Tangent Space at a Point85
6.2 Smooth Points92
6.3 Smoothness in Families96
6.4 Bertini's Theorem99
6.5 The Gauss Mapping102
7 Birational Geometry105
7.1 Resolution of Singularities105
7.2 Rational Maps112
7.3 Birational Equivalence114
7.4 Blowing Up Along an Ideal115
7.5 Hypersurfaces119
7.6 The Classification Problems120
8 Maps to Projective Space123
8.1 Embedding a Smooth Curve in Three-Space124
8.2 Vector Bundles and Line Bundles127
8.3 The Sections of a Vector Bundle129
8.4 Examples of Vector Bundles131
8.5 Line Bundles and Rational Maps136
8.6 Very Ample Line Bundles141
A Sheaves and Abstract Algebraic Varieties145
A.1 Sheaves145
A.2 Abstract Algebraic Varieties150
References153
Index157