On the three dimensional minimal model program in positive characteristic

Hacon, Christopher; Xu, Chenyang

doi:10.1090/S0894-0347-2014-00809-2

On the three dimensional minimal model program in positive characteristic
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by Christopher D. Hacon and Chenyang Xu;

J. Amer. Math. Soc. 28 (2015), 711-744

DOI: https://doi.org/10.1090/S0894-0347-2014-00809-2

Published electronically: June 4, 2014

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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 $\{ 1-\frac 1n|n\in \mathbb N\}$, 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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