Reduction maps and minimal model theory

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 (K X+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. © 2012 The Author(s).