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