Existence of log canonical flips and a special LMMP

Abstract

Let $(X/Z,B+A)$ be a $\Q$-factorial dlt pair where $B,A\ge 0$ are $\Q$-divisors and $K_X+B+A\sim_\Q 0/Z$. 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.

40 pages. Reorganised, exposition improved, also includes preprint arXiv:1104.4979v1. The main result is now unconditional thanks to Hacon and Xu who generalise a result of Fujino and Gongyo on semi-log canonical pairs that is used in this paper. To appear in Pub. Math. de l'IHÉS

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Cited by in corpus (4)

• On Finiteness of B-representation and Semi-log Canonical Abundance
• Existence of log canonical closures
• Divisorial algebras and modules on schemes
• Grothendieck--Lefschetz type theorems for the local Picard group