Uniform bounds for strongly $F$-regular surfaces

TL;DR

This paper proves that two-dimensional Kawamata log terminal pairs over algebraically closed fields of large characteristic are also strongly $F$-regular, establishing a connection between these singularity types in positive characteristic.

Contribution

It demonstrates that for sufficiently large characteristic, Kawamata log terminal pairs in dimension two are strongly $F$-regular, linking these concepts in algebraic geometry.

Findings

KLT pairs are strongly $F$-regular in large characteristic

The characteristic bound depends only on the coefficients of $B$

Establishes a uniform bound for strong $F$-regularity in dimension two

Abstract

We show that if $(X,B)$ is a two dimensional Kawamata log terminal pair defined over an algebraically closed field of characteristic $p$, and $p$ is sufficiently large, depending only on the coefficients of $B$, then $(X,B)$ is also strongly $F$-regular.