Introduction to the log minimal model program for log canonical pairs

Abstract

We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Kollár's vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone and contraction theorems for quasi-log varieties, especially, for log canonical pairs.

158 pages. This version is the same as Kyoto-Math 2009-03. It is a completely revised and expanded version of arXiv:0705.2075 and arXiv:0705.2076