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; and Riemann-Roch
theorems.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
CBMS Regional Conference Series in Mathematics |
Release date: |
December 1984 |
Authors: |
William Fulton
|
Dimensions: |
253 x 178 x 6mm (L x W x T) |
Format: |
Paperback
|
ISBN-13: |
978-0-8218-0704-0 |
Categories: |
Books
|
LSN: |
0-8218-0704-8 |
Barcode: |
9780821807040 |
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