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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.
@article{PMIHES_2012__115__325_0,
author = {Birkar, Caucher},
title = {Existence of log canonical flips and a special {LMMP}},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {325--368},
publisher = {Springer-Verlag},
volume = {115},
year = {2012},
doi = {10.1007/s10240-012-0039-5},
zbl = {1256.14012},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-012-0039-5/}
}
TY - JOUR AU - Birkar, Caucher TI - Existence of log canonical flips and a special LMMP JO - Publications Mathématiques de l'IHÉS PY - 2012 SP - 325 EP - 368 VL - 115 PB - Springer-Verlag UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-012-0039-5/ DO - 10.1007/s10240-012-0039-5 LA - en ID - PMIHES_2012__115__325_0 ER -
%0 Journal Article %A Birkar, Caucher %T Existence of log canonical flips and a special LMMP %J Publications Mathématiques de l'IHÉS %D 2012 %P 325-368 %V 115 %I Springer-Verlag %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-012-0039-5/ %R 10.1007/s10240-012-0039-5 %G en %F PMIHES_2012__115__325_0
Birkar, Caucher. Existence of log canonical flips and a special LMMP. Publications Mathématiques de l'IHÉS, Tome 115 (2012), pp. 325-368. doi: 10.1007/s10240-012-0039-5
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