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Reduction maps and minimal model theory

Part of: Birational geometry

Published online by Cambridge University Press:  04 December 2012

Yoshinori Gongyo  and
Brian Lehmann
Yoshinori Gongyo
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan (email: gongyo@ms.u-tokyo.ac.jp)
Brian Lehmann
Affiliation:
Department of Mathematics, Rice University, Houston, TX 77005, USA (email: blehmann@rice.edu)
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Abstract

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We use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a Kawamata log terminal pair (X,Δ) can be detected on a birational model of the base of the (KX+Δ)-trivial reduction map. We then interpret the main conjectures of the minimal model program as a natural statement about the existence of curves on X.

Keywords

minimal modelabundance conjecturereduction map

MSC classification

Secondary: 14E30: Minimal model program (Mori theory, extremal rays)
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 2 , February 2013 , pp. 295 - 308
Copyright
© The Author(s) 2012

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