Reduction maps and minimal model theory

By Yoshinori Gongyo, Brian Lehmann. Compositio Mathematica, 2011

48 citations recorded by the source corpus.

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 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/00669fddfddd3bdff88d8e8c4c5c74d626f945f3