Log minimal models according to Shokurov

Birkar, Caucher

doi:10.2140/ant.2009.3.951

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Log minimal models according to Shokurov

Caucher Birkar

Vol. 3 (2009), No. 8, 951–958

DOI: 10.2140/ant.2009.3.951

Abstract

Following Shokurov’s ideas, we give a short proof of the following klt version of his result: termination of terminal log flips in dimension $d$ implies that any klt pair of dimension $d$ has a log minimal model or a Mori fibre space. Thus, in particular, any klt pair of dimension $4$ has a log minimal model or a Mori fibre space.

Keywords

minimal models, Mori fibre spaces

Mathematical Subject Classification 2000

Primary: 14E30

Milestones

Received: 12 March 2009

Revised: 7 September 2009

Accepted: 6 October 2009

Published: 25 December 2009

Authors

Caucher Birkar
DPMMS, Centre for Mathematical Sciences Cambridge University Wilberforce Road Cambridge, CB3 0WB United Kingdom

Vol. 3, No. 8, 2009