English

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

Algebraic Geometry 2014-10-17 v2

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\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\Q-divisor; semi-ampleness holds for a nef and big \Q\Q-divisor DD if D(KX+B)D-(K_X+B) is nef and big and (X,B)(X,B) is projective klt; \Q\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.

Keywords

Cite

@article{arxiv.1311.3098,
  title  = {Existence of flips and minimal models for 3-folds in char p},
  author = {Caucher Birkar},
  journal= {arXiv preprint arXiv:1311.3098},
  year   = {2014}
}

Comments

48 pages, final version to appear in Annales Scientifiques de l'ENS