Birational Geometry of Algebraic Varieties (Cambridge Tracts in Mathematics) by Janos Kollár

Cambridge Tracts in Mathematics #134

by Janos Kollár

One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.

Genres: Mathematics

Hardcover

First published September 17, 1998

Reviews

[Andrew]

As another reviewer said, this book is more demanding than it advertises. Before reading this book, it's good to already have a rough understanding of why singularities must be considered for the minimal model program to work. With the right mindset, this book does a good job at motivating the wide variety of singularity types that appear in the minimal model program.

[Carsten · Rating 4 out of 5]

Quite demanding. The required prerequisite is Hartshorne. I don't think so. For the vanishing theorems you should compare Lazarsfeld.