English

On the three dimensional minimal model program in positive characteristic

Algebraic Geometry 2013-06-28 v2

Abstract

Let f:(X,B)Zf:(X,B)\to Z be a 3-fold extremal dlt flipping contraction defined over an algebraically closed field of characteristic p>5p>5, such that the coefficients of {B}\{B\} are in the standard set {11nnN}\{1-\frac 1n|n\in \mathbb N\}, then the flip of ff exists. As a consequence, we prove the existence of minimal models for any projective \Q\Q-factorial terminal variety XX with pseudo-effective canonical divisor KXK_X.

Keywords

Cite

@article{arxiv.1302.0298,
  title  = {On the three dimensional minimal model program in positive characteristic},
  author = {Christopher D. Hacon and Chenyang Xu},
  journal= {arXiv preprint arXiv:1302.0298},
  year   = {2013}
}

Comments

We correct some typos and inaccuracies, improve a result and add some applications

R2 v1 2026-06-21T23:19:29.397Z