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

preprint2014arXivOpen access

Abstract

We will prove the following results for 33-fold pairs (X,B)(X,B) over an algebraically closed field kk of characteristic p>5p>5: log flips exist for $\Q$-factorial dlt pairs (X,B)(X,B); log minimal models exist for projective klt pairs (X,B)(X,B) with pseudo-effective KX+BK_X+B; the log canonical ring R(KX+B)R(K_X+B) is finitely generated for projective klt pairs (X,B)(X,B) when KX+BK_X+B is a big $\Q$-divisor; semi-ampleness holds for a nef and big $\Q$-divisor DD if D−(KX+B)D-(K_X+B) is nef and big and (X,B)(X,B) is projective klt; $\Q$-factorial dlt models exist for lc pairs (X,B)(X,B); terminal models exist for klt pairs (X,B)(X,B); ACC holds for lc thresholds; etc.

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