Birational Geometry of Algebraic Varieties
Birational Geometry of Algebraic Varieties
One of the major discoveries of the last two decades of the twentieth century 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 a 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.
- Unique treatment
- Suitable for non-experts
- Author is Field's medalist (mathematical equivalent of the Nobel Prize)
Reviews & endorsements
"The book under review, written by two of the leaders in the field, is a comprehensive treatment of the minimal model program...invaluable for the more advanced student of the minimal model program, as well as researchers in the field." Mathematical Reviews
"...this book, written by two of the main players in this development, answers a demand for a long awaited introductory textbook for the beginners in this field. The expositon is sufficiently elementary, self-contained and comprehensive, and requires fewer prerequisites, so this book will become a standard reference." Bulletin of the American Mathematical Society
Product details
February 2008Paperback
9780521060226
264 pages
228 × 152 × 17 mm
0.429kg
Available
Table of Contents
- 1. Rational curves and the canonical class
- 2. Introduction to minimal model program
- 3. Cone theorems
- 4. Surface singularities
- 5. Singularities of the minimal model program
- 6. Three dimensional flops
- 7. Semi-stable minimal models.
