Existence of flips for generalized lc pairs

Abstract

We prove the existence of flips for $\mathbb{Q}$-factorial NQC generalized lc pairs, and the cone and contraction theorems for NQC generalized lc pairs. This answers a question of C. Birkar which was conjectured by J. Han and Z. Li. As an immediate application, we show that we can run the minimal model program for $\mathbb{Q}$-factorial NQC generalized lc pairs. In particular, we complete the minimal model program for $\mathbb{Q}$-factorial NQC generalized lc pairs in dimension $\le 3$ and pseudo-effective $\mathbb{Q}$-factorial NQC generalized lc pairs in dimension $4$.

38 pages, v3. Comments are welcome. Proof of Theorem 1.1 has been greatly simplified