《代數幾何(第1卷):復射影簇》是時下為數不多的代數幾何的經典教材之一，已被眾多學校用做教學參考書。與《代數幾何(第1卷):復射影簇》相配套的教材《The Red Book of Varieties and Schemes》和《Algebraic Geometry GTM52》也已影印出版。代數幾何是近代以來發展迅速的一門數學的分支學科，與其他領域的許多學科有著緊密的聯繫，也是高等院校數學專業研究生階段所開設的一門非常重要的基礎課程。《代數幾何(第1卷):復射影簇》是由作者多年來在各處講授代數幾何課的筆記，經多次修訂後整理成冊。《代數幾何(第1卷):復射影簇》的前一部分主要介紹了復射影簇，後一部分則重點探討了概型，內容包括概型的凝聚層的上同調與套用。《代數幾何(第1卷):復射影簇》適用於數學專業的二年級研究生及需要相關知識的其他領域的專家學者。
基本介紹
- 書名：代數幾何:復射影簇
- 出版社：世界圖書出版公司
- 頁數：186頁
- 開本：24
- 定價：29.00
- 作者：姆佛爾德 (Mumford.D)
- 出版日期：2008年11月1日
- 語種：英語
- ISBN：9787506292122
- 品牌：世界圖書出版公司北京公司
基本介紹,內容簡介,作者簡介,圖書目錄,文摘,
基本介紹
內容簡介
《代數幾何(第1卷):復射影簇》由世界圖書出版公司出版。
作者簡介
作者：(英國)姆佛爾德 (Mumford.D)
圖書目錄
Introduction
Prerequisites
Chapter 1. Affine Varieties
1A. Their Definition, Tangent Space, Dimension, Smooth and Singular Points.
1B. Analytic Uniformization at Smooth Points, Examples of Topological Knottedness at Singular Points
1C. Ox,xa UFD when x Smooth; Divisor of Zeroes and Poles of Functions
Chapter 2. Projective Varieties
2A. Their Definition, Extension of Concepts from Aftine to Projective Case
2B. Products, Segre Embedding, Correspondences
2C. Elimination Theory, Noether's Normalization Lemma, Density of Zariski-Open Sets
Chapter 3. Structure of Correspondences
3A. Local Properties——Smooth Maps, Fundamental Openness Principle, Zariski's Main Theorem
3B. Global Propcrties——Zariski's Connectedness Theorem, Specialization Principle
3C. Intersections on Smooth Varieties
Chapter 4. Chow's Theorem
4A. Internally and Externally Defined Analytic Sets and their Local Descriptions as Branched Coverings of C'.
4B. Applications to Uniqueness of Algebraic Structure and Connectedness
Chapter 5. Degree of a Projective Variety
5A. Definition of deg X, multxX, of the Blow up Bx(X), Effect of a Projection, Examples
5B. Bezout's Theorem
5C. Volume of a Projective Variety; Review of Homology, DeRham's Theorem, Varieties as Minimal Submanifolds
Chapter 6. Linear Systems
6A. The Correspondence between Linear Systems and Rational Maps, Examples; Complete Linear Systems are Finite-Dimensional
6B. Differential Forms, Canonical Divisors and Branch Loci
6C. Hilbert Polynomials, Relations with Degree
Appendix to Chapter 6. The Weil-Samuel Algebraic Theory of Multiplicity
Chapter 7. Curves and Their Genus
7A. Existence and Uniqueness of the Non-Singular Model of Each Function Field of Transcendence Degree 1 (after Albanese)
7B.Arithmetic Genus = Topological Genus; Existence of Good Projections to p1, p2, p3
7C. Residues of Differentials on Curves, the Classical Riemann-Roch Theorem for Curves and Applications
7D. Curves of Genus 1 as Plane Cubics and as Complex Tori C/L
Chapter 8. The Birational Geometry of Surfaces
8A. Generalities on Blowing up Points
8B. Resolution of Singularities of Curves on a Smooth Surface by Blowing up the Surface; Examples
8C. Factorization of Birational Maps between Smooth Surfaces; the Trees of Infinitely Near Points
8D. The Birational Map between P" and the Quadric and Cubic Surfaces; the 27 Lines on a Cubic Surface
Bibliography
List of Notations
Index
Prerequisites
Chapter 1. Affine Varieties
1A. Their Definition, Tangent Space, Dimension, Smooth and Singular Points.
1B. Analytic Uniformization at Smooth Points, Examples of Topological Knottedness at Singular Points
1C. Ox,xa UFD when x Smooth; Divisor of Zeroes and Poles of Functions
Chapter 2. Projective Varieties
2A. Their Definition, Extension of Concepts from Aftine to Projective Case
2B. Products, Segre Embedding, Correspondences
2C. Elimination Theory, Noether's Normalization Lemma, Density of Zariski-Open Sets
Chapter 3. Structure of Correspondences
3A. Local Properties——Smooth Maps, Fundamental Openness Principle, Zariski's Main Theorem
3B. Global Propcrties——Zariski's Connectedness Theorem, Specialization Principle
3C. Intersections on Smooth Varieties
Chapter 4. Chow's Theorem
4A. Internally and Externally Defined Analytic Sets and their Local Descriptions as Branched Coverings of C'.
4B. Applications to Uniqueness of Algebraic Structure and Connectedness
Chapter 5. Degree of a Projective Variety
5A. Definition of deg X, multxX, of the Blow up Bx(X), Effect of a Projection, Examples
5B. Bezout's Theorem
5C. Volume of a Projective Variety; Review of Homology, DeRham's Theorem, Varieties as Minimal Submanifolds
Chapter 6. Linear Systems
6A. The Correspondence between Linear Systems and Rational Maps, Examples; Complete Linear Systems are Finite-Dimensional
6B. Differential Forms, Canonical Divisors and Branch Loci
6C. Hilbert Polynomials, Relations with Degree
Appendix to Chapter 6. The Weil-Samuel Algebraic Theory of Multiplicity
Chapter 7. Curves and Their Genus
7A. Existence and Uniqueness of the Non-Singular Model of Each Function Field of Transcendence Degree 1 (after Albanese)
7B.Arithmetic Genus = Topological Genus; Existence of Good Projections to p1, p2, p3
7C. Residues of Differentials on Curves, the Classical Riemann-Roch Theorem for Curves and Applications
7D. Curves of Genus 1 as Plane Cubics and as Complex Tori C/L
Chapter 8. The Birational Geometry of Surfaces
8A. Generalities on Blowing up Points
8B. Resolution of Singularities of Curves on a Smooth Surface by Blowing up the Surface; Examples
8C. Factorization of Birational Maps between Smooth Surfaces; the Trees of Infinitely Near Points
8D. The Birational Map between P" and the Quadric and Cubic Surfaces; the 27 Lines on a Cubic Surface
Bibliography
List of Notations
Index
文摘
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