Intersection theory相交理论 第2版
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作者： William Fulton著
出 版 社：
出版时间： 1998-6-1字数：版次： 1页数： 470印刷时间： 1998/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387985497包装： 平装内容简介
From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. The aim of this book is to develop the foundations of this theory, and to indicate the range of classical and modern applications. Although a comprehensive history of this vast subject is not attempted, the author points out some of the striking early appearances of the ideas of intersection theory. A suggested prerequisite for the reading of this book is a first course in algebraic geometry. Fulton's introduction to intersection theory has been well used for more than 10 years. It is still the only existing complete modern treatise of the subject and received the Steele Prize for best exposition in August 1996.
目录
Introduction
Chapter 1 Rational Equivalence
Chapter 2 Divisors
Chapter 3 Vector Bundles and Chern Classes
Chapter 4 Cones and Segre Classes
Chapter 5 Deformation to the Normal Cone
Chapter 6 Intersection Products
Chapter 7 Intersection Multiplicities
Chapter 8 Intersections on Non-singular Varieties
Chapter 9 Excess and Residual Intersections
Chapter 10 Families of Algebraic Cycles
Chapter 11 Dynamic Intersections
Chapter 12 Positivity
Chapter 13 Rationality
Chapter 14 Degeneracy Loci and Grassmannians
Chapter 15 Riemann-Roch for Non-singular Varieties
Chapter 16 Correspondences
Chapter 17 Bivariant Intersection Theory
Chapter 18 Riemann-Roch for Singular Varieties
Chapter 19 Algebraic, Homological and Numerical Equivalence
Chapter 20 Generalizations
App. A Algebra
App. B Algebraic Geometry (Glossary)
Bibliography
Notation
Index
