On the three dimensional minimal model program in positive characteristic

TL;DR

This paper proves the existence of flips and minimal models for certain 3-dimensional algebraic varieties in positive characteristic, advancing the minimal model program in this setting.

Contribution

It establishes the existence of flips for 3-fold extremal dlt contractions over fields with characteristic greater than 5, and proves minimal model existence for specific varieties.

Findings

Existence of flips for 3-fold extremal dlt contractions in characteristic p>5

Minimal models exist for projective Q-factorial terminal varieties with pseudo-effective canonical divisor

Advances the minimal model program in positive characteristic

Abstract

Let $f:(X,B)\to Z$ be a 3-fold 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 $\Q$-factorial terminal variety $X$ with pseudo-effective canonical divisor $K_X$.