Fundamental theorems for the log minimal model program

Abstract

In this paper, we prove the cone theorem and the contraction theorem for pairs $(X, B)$, where $X$ is a normal variety and $B$ is an effective $\mathbb R$-divisor on $X$ such that $K_X+B$ is $\mathbb R$-Cartier.

64 pages. This is a slightly revised version of Kyoto-Math 2009-25, v2: Theorem 10.5 is new, minor modifications, v3: minor modifications, Theorem 18.10 is new