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Introduction to Intersection Theory in Algebraic Geometry
William Fulton, University of Chicago, IL
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
1984; 83 pp; softcover
Number: 54
Reprint/Revision History:
third printing with corrections 1996; fourth printing 1999
ISBN-10: 0-8218-0704-8
ISBN-13: 978-0-8218-0704-0
List Price: US$28
Member Price: US$22.40
All Individuals: US$22.40
Order Code: CBMS/54
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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.

Readership

Graduate students and research mathematicians interested in algebraic geometry.

Reviews

"These notes have maintained their outstanding role as both a beautiful introduction and a masterly survey in this area of algebraic geometry. Now as before, W. Fulton's introductory notes are an excellent invitation to this subject, and a valuable spring of information for any mathematician interested in the methods of algebraic geometry in general."

-- Zentralblatt MATH

Table of Contents

  • Intersections of hypersurfaces
  • Multiplicity and normal cones
  • Divisors and rational equivalence
  • Chern classes and Segre classes
  • Gysin maps and intersection rings
  • Degeneracy Loci
  • Refinements
  • Positivity
  • Riemann-Roch
  • Miscellany
  • References
  • Notes (1983-1995)
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