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Reduction maps and minimal model theory
Part of
- Birational geometry
Yoshinori Gongyo, Brian Lehmann
Journal:

Compositio Mathematica / Volume 149 / Issue 2 / February 2013

Published online by Cambridge University Press:

04 December 2012, pp. 295-308

Print publication:

February 2013
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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.

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Reduction maps and minimal model theory