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On the log discrepancies in toric Mori contractions


Authors: Valery Alexeev and Alexander Borisov
Journal: Proc. Amer. Math. Soc. 142 (2014), 3687-3694
MSC (2010): Primary 14E30, 14M25
Published electronically: July 3, 2014
MathSciNet review: 3251710
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Abstract: It was conjectured by McKernan and Shokurov that for all Mori contractions from $ X$ to $ Y$ of given dimensions, for any positive $ \eps $ there is a positive $ \delta $ such that if $ X$ is $ \eps $-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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Additional Information

Valery Alexeev
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30605
Email: valery@math.uga.edu

Alexander Borisov
Affiliation: Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: borisov@pitt.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12159-9
Received by editor(s): November 16, 2012
Published electronically: July 3, 2014
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.