**CBMS Regional Conference Series in Mathematics**

Volume: 54;
1984;
83 pp;
Softcover

MSC: Primary 14; 13;

Print ISBN: 978-0-8218-0704-0

Product Code: CBMS/54

List Price: $30.00

Individual Price: $24.00

**Electronic ISBN: 978-1-4704-2416-9
Product Code: CBMS/54.E**

List Price: $30.00

Individual Price: $24.00

# Introduction to Intersection Theory in Algebraic Geometry

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*William Fulton*

A co-publication of the AMS and CBMS

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.

#### Table of Contents

# Table of Contents

## Introduction to Intersection Theory in Algebraic Geometry

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents vii8 free
- Preface ix10 free
- Chapter 1. Intersections of Hypersurfaces 112 free
- Chapter 2. Multiplicity and Normal Cones 920
- Chapter 3. Divisors and Rational Equivalence 1930
- Chapter 4. Chern Classes and Segre Classes 2940
- Chapter 5. Gysin Maps and Intersection Rings 3748
- Chapter 6. Degeneracy Loci 4758
- Chapter 7. Refinements 5364
- Chapter 8. Positivity 5970
- Chapter 9. Riemann-Roch 6374
- Chapter 10. Miscellany 6980
- References 7586
- Notes (1983-1995) 7788
- Back Cover Back Cover197

#### 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