Birational Geometry of Algebraic Varieties

This book provides the first comprehensive introduction to the circle of ideas developed around Mori's program.

Janos Kollár (Author), Shigefumi Mori (Author)

9780521060226, Cambridge University Press

Paperback / softback, published 4 February 2008

264 pages
22.8 x 15.2 x 1.7 cm, 0.429 kg

Review of the hardback: '… a very good survey of present research … a very clear presentation of the subject.' EMS

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.

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.

Subject Areas: Algebraic geometry [PBMW]