文档介绍：133
Graduate Texts in Mathematics
Editorial Board
. Ewing . Gehring . Halmos
Joe Harris
Algebraic Geometry
A First Course
With 83 Illustrations
Springer-Verlag
New York Berlin Heidelberg London Paris
Tokyo Hong Kong Barcelona Budapest
Preface
This book is based on one-semester courses given at Harvard in 1984, at Brown in
1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first
introduction to the subject. Even so, a few words are in order about the purposes
of the book.
Algebraic geometry has developed tremendously over the last century. During
the 19th century, the subject was practiced on a relatively concrete, down-to-earth
level; the main objects of study were projective varieties, and the techniques for the
most part were grounded in geometric constructions. This approach flourished
during the middle of the century and reached its culmination in the work of the
Italian school around the end of the 19th and the beginning of the 20th centuries.
Ultimately, the subject was pushed beyond the limits of its foundations: by the end
of its period the Italian school had progressed to the point where the language and
techniques of the subject could no longer serve to express or carry out the ideas of
its best practitioners.
This was more than amply remedied in the course of several developments
beginning early in this century. To begin with, there was the pioneering work of
Zariski who, aided by the German school of abstract algebraists, eeded in
putting the subject on a firm algebraic foundation. Around the same time, Weil
introduced the notion of abstract algebraic variety, in effect redefining the basic
objects studied in the subject. Then in the 1950s came Serre’s work, introducing the
fundamental tool of sheaf theory. Finally (for now), in the 196Os, Grothendieck
(aided and abetted by Artin, Mumford, and many others) introduced the concept
of the scheme. Th