Finite generation of the log canonical ring for 3-folds in char $p$

TL;DR

This paper proves the finite generation of the log canonical ring for 3-dimensional klt pairs over algebraically closed fields of characteristic p>5, advancing the understanding of minimal model programs in positive characteristic.

Contribution

It establishes finite generation of the log canonical ring for 3-folds in characteristic p>5 and proves log abundance for certain cases, filling gaps in positive characteristic algebraic geometry.

Findings

Finite generation of the log canonical ring for 3-folds in characteristic p>5.

Proof of log abundance for kappa=2 in this setting.

Progress towards minimal model program in positive characteristic.

Abstract

We prove that the log canonical ring of a klt pair of dimension $3$ with $\mathbb{Q}$-boundary over an algebraically closed field of characteristic $p>5$ is finitely generated. In the process we prove log abundance for such pairs in the case $\kappa=2$.