On the log discrepancies in toric Mori contractions

Alexeev, Valery; Borisov, Alexander

doi:10.1090/S0002-9939-2014-12159-9

On the log discrepancies in toric Mori contractions
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by Valery Alexeev and Alexander Borisov PDF

Proc. Amer. Math. Soc. 142 (2014), 3687-3694 Request permission

Abstract:

It was conjectured by M^cKernan 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.

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