Introduction to Intersection Theory in Algebraic Geometry (Cbms Regional Conference Series in Mathematics) - Softcover

William Fulton

Softcover

ISBN 10: 0821807048 ISBN 13: 9780821807040

Publisher: American Mathematical Society, 1984

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1984
• Language: English
• ISBN 10: 0821807048
• ISBN 13: 9780821807040
• Binding: Paperback
• Number of pages: 83