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Letters of a Bi-rationalist. VII Ordered termination

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Abstract

To construct a resulting model in the LMMP, it is sufficient to prove the existence of log flips and their termination for some sequences. We prove that the LMMP in dimension d − 1 and the termination of terminal log flips in dimension d imply, for any log pair of dimension d, the existence of a resulting model: a strictly log minimal model or a strictly log terminal Mori log fibration, and imply the existence of log flips in dimension d + 1. As a consequence, we prove the existence of a resulting model of 4-fold log pairs, the existence of log flips in dimension 5, and Geography of log models in dimension 4.

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

    V. V. Shokurov

  2. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. V. Shokurov

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  1. V. V. Shokurov
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Correspondence to V. V. Shokurov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 184–208.

To V.A. Iskovskikh, who has greatly shaped my vision of mathematics

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Shokurov, V.V. Letters of a Bi-rationalist. VII Ordered termination. Proc. Steklov Inst. Math. 264, 178–200 (2009). https://doi.org/10.1134/S0081543809010192

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