Smith J. Introduction to Algebraic Geometry 2014

Textbook in PDF format

This book is intended for self-study or as a textbook for graduate students or advanced undergraduates. It presupposes some basic knowledge of pointset topology and a solid foundation in linear algebra. Otherwise, it develops all of the commutative algebra, sheaf-theory and cohomology needed to understand the material. This is the kind of background students might have at a school that emphasizes applied mathematics, or one where enrollment is not sufficient to run separate courses in commutative algebra.
A classical result
Affine varieties
Local properties of affine varieties
Varieties and Schemes
Projective varieties
Curves
Appendixes
Algebra
Sheaves and ringed spaces
Cohomology
Solutions to Selected Exercises