Synopses & Reviews
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.
Review
Review of 1st Edition "...This text, with its brilliant content and excellently arranged, is a prime mover in algebraic geometry, and a must for each algebraic geometer! It is an indispensable reference book, an outstanding textbook, and a great source for geometric research in the future." -- MATHEMATICAL REVIEWS
Synopsis
The aim of this book is to develop the foundations of intersection 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 this theory.
Synopsis
Intersection theory has played a central role in mathematics, from the ancient origins of algebraic geometry in the solutions of polynomial equations to the triumphs of algebraic geometry during the last two centuries. This book develops the foundations of the theory and indicates the range of classical and modern applications. The hardcover edition received the prestigious Steele Prize in 1996 for best exposition.
Table of Contents
Rational Equivalence.- Divisors.- Vector Bundles.- Cones and Segre Classes.- Deformations to the Normal Cone.- Intersection Products.- Intersection Multiplicites.- Intersections on Non-singular Varieties.- Excess and Residual Intersections.- Families of Algebraic Cycles.- Dynamic Intersections.- Positivity.- Rationality.- Degeneracy Loci and Grassmannians.- Riemann-Roch for Non-singular Varieties.- Correspondences.- Bivariant Intersections Theory.- Riemann-Roch for Singular Varieties.- Algebraic: Homological and Numerical Equivalence.- Generalizations.