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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On the three dimensional minimal model program in positive characteristic
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by Christopher D. Hacon and Chenyang Xu PDF
J. Amer. Math. Soc. 28 (2015), 711-744 Request permission


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 $\{ 1-\frac 1n|n\in \mathbb N\}$, 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
  • MR Author ID: 613883
  • Email:
  • Chenyang Xu
  • Affiliation: Beijing International Center of Mathematics Research, 5 Yiheyuan Road, Haidian District, Beijing, 100871, China
  • Email:
  • 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
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 28 (2015), 711-744
  • MSC (2010): Primary 14E30; Secondary 14E05, 14J30, 13A35
  • DOI:
  • MathSciNet review: 3327534