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arXiv · 1103.1605

Reduction maps and minimal model theory

Yoshinori Gongyo·Brian Lehmann
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Abstract

We use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a klt pair $(X,\Delta)$ can be detected on the base of the $(K_{X}+\Delta)$-trivial reduction map. Thus we show that the main conjectures of the minimal model program can be interpreted as a natural statement on the existence of curves on $X$.

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Yoshinori Gongyo, Brian Lehmann. 2011-03-08. Reduction maps and minimal model theory. https://doi.org/10.1112/s0010437x12000553

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