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

On the Log Discrepancies in Toric Mori Contractions