Existence of log canonical flips and a special LMMP

Abstract

Let (X/Z,B+A) be a Q-factorial dlt pair where B,A≥0 are Q-divisors and K X +B+A∼ Q 0/Z. We prove that any LMMP/Z on K X +B with scaling of an ample/Z divisor terminates with a good log minimal model or a Mori fibre space. We show that a more general statement follows from the ACC for lc thresholds. An immediate corollary of these results is that log flips exist for log canonical pairs.