Existence of log canonical flips and a special LMMP

Details Existence of log canonical flips and a special LMMP Existence of log canonical flips and a special LMMP

2011-04-26

arxiv.org/abs/1104.4981v3

Mathematics

Algebraic Geometry

40 pages. Reorganised, exposition improved, also includes preprint arXiv:1104.4979v1. The main result is now unconditional tha

Scientific paper

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.

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