Log minimal models according to Shokurov

Caucher Birkar

doi:10.2140/ant.2009.3.951

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Home > Journals > Algebra Number Theory > Volume 3 > Issue 8 > Article

2009 Log minimal models according to Shokurov

Caucher Birkar

Algebra Number Theory 3(8): 951-958 (2009). DOI: 10.2140/ant.2009.3.951

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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.