ENGLISH

Introduction to Intersection Theory in Algebraic Geometry

By William Fulton

Book information

Publisher
American Mathematical Society
Year
1984
ISBN
0821807048, 9780821807040
LCC
QA1,QA564
Open Library ID
OL22585489M
Language
english
Format
PDF
Filesize
4 MB (4188041 bytes)
Series
Cbms Regional Conference Series in Mathematics
Pages
83\89
Time added
2011-04-20 14:05:05

Description

This book introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. It requires little technical background: much of the material is accessible to graduate students in mathematics. A broad survey, the book touches on many topics, most importantly introducing a powerful new approach developed by the author and R. MacPherson. It was written from the expository lectures delivered at the NSF-supported CBMS conference at George Mason University, held June 27-July 1, 1983. The author describes the construction and computation of intersection products by means of the geometry of normal cones. In the case of properly intersecting varieties, this yields Samuel's intersection multiplicity; at the other extreme it gives the self-intersection formula in terms of a Chern class of the normal bundle; in general it produces the excess intersection formula of the author and R. MacPherson. Among the applications presented are formulas for degeneracy loci, residual intersections, and multiple point loci; dynamic interpretations of intersection products; Schubert calculus and solutions to enumerative geometry problems; Riemann-Roch theorems.

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