On the three dimensional minimal model program in positive characteristic

Hacon, Christopher¹ ; Xu, Chenyang²

¹ Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 48112-0090
² Beijing International Center of Mathematics Research, 5 Yiheyuan Road, Haidian District, Beijing, 100871, China

Journal of the American Mathematical Society, Tome 28 (2015) no. 3, pp. 711-744

Résumé

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 $K_X$.

Détail

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

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