Existence of log canonical flips and a special LMMP

@article{Birkar2011ExistenceOL,
  title={Existence of log canonical flips and a special LMMP},
  author={Caucher Birkar},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2011},
  volume={115},
  pages={325-368}
}
  • C. Birkar
  • Published 2011
  • Mathematics
  • Publications mathématiques de l'IHÉS
Let (X/Z,B+A) be a Q-factorial dlt pair where B,A≥0 are Q-divisors and KX+B+A∼Q0/Z. We prove that any LMMP/Z on KX+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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