The LMMP for log canonical 3-folds in char $p$

TL;DR

This paper establishes the feasibility of running the log minimal model program for log canonical 3-fold pairs in characteristic p>5, including key theorems and the existence of flips and minimal models.

Contribution

It proves the Cone and Contraction Theorems, existence of flips, and minimal models for log canonical 3-fold pairs in characteristic p>5, advancing the minimal model program in positive characteristic.

Findings

Proved the Cone Theorem in characteristic p>5

Established the existence of flips for log canonical 3-folds

Showed certain log minimal models are good

Abstract

We prove that one can run the log minimal model program for log canonical $3$-fold pairs in characteristic $p>5$. In particular we prove the Cone Theorem, Contraction Theorem, the existence of flips and the existence of log minimal models for pairs with log divisor numerically equivalent to an effective divisor. These follow from our main results, which are that certain log minimal models are good.