Existence of flips and minimal models for 3-folds in char p

By C. Birkar. 2013

126 citations recorded by the source corpus.

We will prove the following results for $3$-fold pairs $(X,B)$ over an algebraically closed field $k$ of characteristic $p>5$: log flips exist for $\Q$-factorial dlt pairs $(X,B)$; log minimal models exist for projective klt pairs $(X,B)$ with pseudo-effective $K_X+B$; the log canonical ring $R(K_X+B)$ is finitely generated for projective klt pairs $(X,B)$ when $K_X+B$ is a big $\Q$-divisor; semi-ampleness holds for a nef and big $\Q$-divisor $D$ if $D-(K_X+B)$ is nef and big and $(X,B)$ is projective klt; $\Q$-factorial dlt models exist for lc pairs $(X,B)$; terminal models exist for klt pairs $(X,B)$; ACC holds for lc thresholds; etc.

View Paper: https://www.semanticscholar.org/paper/8ed04966cb1b8a7512ec5a676bcf3f5e7713b836

How researchers see this paper

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1. J. Waldron
2. C. Birkar
3. Christopher D. Hacon
4. Y. Odaka
5. H. Blum
6. O. Fujino
7. Yoshinori Gongyo
8. Ingrid Bauer

Citations in the corpus

• Existence of Mori fibre spaces for 3-folds in char $p$ (2014, methodology): “Note that the above definitions are the same as in [3] but slightly different from the traditional definitions in that we allow φ−1 to contract divisors.”