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On the three dimensional minimal model program in positive characteristic


Authors: Christopher D. Hacon and Chenyang Xu
Journal: J. Amer. Math. Soc. 28 (2015), 711-744
MSC (2010): Primary 14E30; Secondary 14E05, 14J30, 13A35
DOI: https://doi.org/10.1090/S0894-0347-2014-00809-2
Published electronically: June 4, 2014
MathSciNet review: 3327534
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Abstract: Let $ f:(X,B)\to Z$ be a threefold extremal dlt flipping contraction defined over an algebraically closed field of characteristic $ p>5$, such that the coefficients of $ \{ B\}$ are in the standard set $ \{ 1-\frac 1n\vert n\in \mathbb{N}\}$, then the flip of $ f$ exists. As a consequence, we prove the existence of minimal models for any projective $ {\mathbb{Q}}$-factorial terminal variety $ X$ with pseudo-effective canonical divisor $ K_X$.


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Additional Information

Christopher D. Hacon
Affiliation: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 48112-0090
Email: hacon@math.utah.edu

Chenyang Xu
Affiliation: Beijing International Center of Mathematics Research, 5 Yiheyuan Road, Haidian District, Beijing, 100871, China
Email: cyxu@math.pku.edu.cn

DOI: https://doi.org/10.1090/S0894-0347-2014-00809-2
Received by editor(s): February 23, 2013
Received by editor(s) in revised form: November 22, 2013, February 12, 2014, and March 27, 2014
Published electronically: June 4, 2014
Article copyright: © Copyright 2014 American Mathematical Society