Algebraic geometry : a first course / Joe Harris

Bibliogr. p. [314]-315. Index

This book consists of two parts, the first entitled "Examples of varieties and maps'' and the second "Attributes of varieties'', and comprises twenty-two lectures (as the chapters are designated) on basic geometrical objects and constructions in classical algebraic geometry; it is based on courses given by the author at Harvard and Brown. It represents his solution to a basic dilemma: on the one hand, the modern approach to algebraic geometry using schemes needs to be learned by anyone wishing to work in the subject; on the other hand, the rather daunting technicalities of scheme theory may overshadow the more approachable classical theory and tend to put people off. As well, by now there are a number of excellent textbooks which mix the classical and modern in a variety of ways and from a variety of perspectives. Given this, the author is surely correct when he argues that the best way to approach the subject is to introduce suitable topics from "elementary'' classical algebraic geometry before going on to the modern theory. The classical theory is, in the author's words, a glorious subject; it is also needed if one is to understand the motivation for schemes and the insight the modern approach gives. (MathSciNet)