Reduction maps and minimal model theory

Details Reduction maps and minimal model theory Reduction maps and minimal model theory

2011-03-08

arxiv.org/abs/1103.1605v2

Mathematics

Algebraic Geometry

19 pages, v2:major revised

Scientific paper

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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