Publications mathématiques de l'IHÉS

, Volume 115, Issue 1, pp 325–368 | Cite as

Existence of log canonical flips and a special LMMP

  • Caucher BirkarEmail author


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.


Exceptional Divisor Ample Divisor Contract Divisor Vertical Case Horizontal Case 
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© IHES and Springer-Verlag 2012

Authors and Affiliations

  1. 1.DPMMS, Centre for Mathematical SciencesCambridge UniversityCambridgeUK

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