Preface

These lectures are designed to provide a survey of modern intersection theory

in algebraie geometry. This theory is the result of many mathematicians' work over

many deeades; the form espoused here was developed with R. MaePherson.

In the first two chapters a few epsisodes are selected from the long history of

intersection theory which illustrate some of the ideas which will be of most concern

to us here. The basic construction of intersection products and Chern classes is

described in the following two chapters. The remaining chapters contain a sampling

of applications and refinements, including theorems of Verdier, Lazarsfeld, Kempf,

Laksov, Gillet, and others.

No attempt is made here to State theorems in their natural generality, to provide

complete proofs, or to cite the literature carefully. We have tried to indicate the

essential points of many of the arguments. Details may be found in [16].

I would like to thank R. Ephraim for organizing the Conference, and C. Ferreira

and the AMS staff for expert help with preparation of the manuscript.

Preface to the 1996 printing

In this revision, we have taken the opportunity to correct some errors and

misprints. In addition, a section of notes has been added, to point out some of the

work that has been done since the first edition was written that is closely related to

ideas discussed in the text. Superscripts in the text refer to these notes. As in the

text, no attempt is made to survey the large and growing literature in intersection

theory.

I am grateful to Jeff Adler for preparing and improving the manuscript and

diagrams.

William Fulton

Chicago, IL

December, 1995