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首页 代数几何入门txt,chm,pdf,epub,mobi下载作者: [英]史密斯 出版社: 世界图书出版公司 原作名: An Invitation to Algebraic Geometry 出版年: 2010-1 页数: 161 定价: 28.00元 丛书: Universitext ISBN: 9787510005152 内容简介 · · · · · ·《代数几何入门(英文版)》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：《代数几何入门(英文版)》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。 目录 · · · · · ·Notes for the Second PrintingPrefaceAcknowledgmentsIndex of Notation1 Affine Algebraic Varieties 1.1 Definition and Examples 1.2 The Zariski Topology 1.3 Morphisms of Affine Algebraic Varieties 1.4 Dimension2 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 Ring3 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 Space4 Quasi-Projective Varieties 4.1 Quasi-Projective Varieties 4.2 A Basis for the Zariski Topology 4.3 Regular Functions5 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 Function6 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 Mapping7 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 Problems8 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 BundlesA Sheaves and Abstract Algebraic Varieties A.1 Sheaves A.2 Abstract Algebraic VarietiesReferencesIndexNotes for the Second PrintingPrefaceAcknowledgmentsIndex of Notation1 Affine Algebraic Varieties 1.1 Definition and Examples 1.2 The Zariski Topology 1.3 Morphisms of Affine Algebraic Varieties 1.4 Dimension2 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 Ring3 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 Space4 Quasi-Projective Varieties 4.1 Quasi-Projective Varieties 4.2 A Basis for the Zariski Topology 4.3 Regular Functions5 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 Function6 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 Mapping7 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 Problems8 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 BundlesA Sheaves and Abstract Algebraic Varieties A.1 Sheaves A.2 Abstract Algebraic VarietiesReferencesIndex · · · · · · () |
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