中文名: 相交理論
原名: Intersection Theory
作者: William Fulton
資源格式: DJVU
版本: 掃描版
出版社: Springer
書號: 0387985492
發行時間: 1998年
地區: 美國
語言: 英文
簡介:

內容簡介:
相交理論在代數幾何的發展中扮演了重要的角色，並至今在許多領域有著重要的應用。本書介紹了相交理論的理論基礎，以及其經典的和現代的應用。雖然在書中沒有著重介紹相交理論的歷史，作者對其在歷史上起到的部分重要作用也有提及。前六章是本書的基礎部分，掌握前六章之後，讀者可以有選擇的閱讀以後的章節。
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.
內容截圖:

目錄:
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