On the Log Discrepancies in Toric Mori Contractions

TL;DR

This paper proves a conjecture relating the log terminal properties of Mori contractions in the toric case, establishing a link between the epsilon-log terminality of the source and the delta-log terminality of the target.

Contribution

It confirms the McKernan-Shokurov conjecture for toric Mori contractions and explores how delta depends on epsilon.

Findings

Conjecture proven in the toric case

Established a relationship between epsilon and delta

Discussed the mysterious dependence of delta on epsilon

Abstract

It was conjectured by McKernan and Shokurov that for all Mori contractions from X to Y of given dimensions, for any positive epsilon there is a positive delta, such that if X is epsilon-log terminal, then Y is delta-log terminal. We prove this conjecture in the toric case and discuss the dependence of delta on epsilon, which seems mysterious.