Literature Guide for Mathematics 535

There are many nice books on Algebraic Geometry, often with different points of view on the subject.

The text for the course is Algebraic Geometry: A First Course by J. Harris, Springer Graduate Texts in Mathematics 133, ISBN 0-387-97716-3. This is a very geometric book starting from some of the classical algebraic varieties which motivated the origins of the subject. This book has many exercises and examples that are useful in getting a feel for algebraic geometry. Here is an excerpt from the Mathematical Reviews discussion of the book:

"... the book succeeds brilliantly ... by concentrating on a number of core topics .... and by treating them in a hugely rich and varied way..."

Read the whole review at the AMS math reviews site.

The following books, as well as a copy of the text, are on reserve in the Mathematics Library in Hill Center:

Algebraic Geometry, R. Hartshorne
This book is a canonical reference to the general theory

Basic algebraic geometry, I. R. Shafarevich

Ideals, varieties and algorithms, D. Cox et al

Using Algebraic Geometry, D. Cox et al

Complex projective varieties I, D. Mumford

The following books may also be useful:

Principles of Algebraic Geometry, P. Griffiths and J. Harris
This deals with the theory of complex varieties by using the topology and differential geometry of complex manifolds

Elementary algebraic geometry, K. Kendig

Introduction to commutative algebra, M. F. Atiyah and I. G. MacDonald

Introduction to algebraic geometry, J. Semple

Schemes : the language of modern algebraic geometry , D. Eisenbud, J. Harris

Commutative algebra with a view toward algebraic geometry,D. Eisenbud

There are online resources available
Algebraic geometry notes of J. Milne's University of Michigan course

Algebraic geometry notes of R. Vakil's Stanford University course