Vol. 3, No. 8, 2009

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Log minimal models according to Shokurov

Caucher Birkar

Vol. 3 (2009), No. 8, 951–958

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.

minimal models, Mori fibre spaces
Mathematical Subject Classification 2000
Primary: 14E30
Received: 12 March 2009
Revised: 7 September 2009
Accepted: 6 October 2009
Published: 25 December 2009
Caucher Birkar
DPMMS, Centre for Mathematical Sciences
Cambridge University
Wilberforce Road
Cambridge, CB3 0WB
United Kingdom