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Existence of log canonical flips and a special LMMP

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Abstract

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.

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  1. DPMMS, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge, CB3 0WB, UK

    Caucher Birkar

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  1. Caucher Birkar
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Birkar, C. Existence of log canonical flips and a special LMMP. Publ.math.IHES 115, 325–368 (2012). https://doi.org/10.1007/s10240-012-0039-5

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  • DOI: https://doi.org/10.1007/s10240-012-0039-5

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