Characterization of two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic

TL;DR

This paper characterizes two-dimensional semi-log canonical hypersurfaces in any characteristic using initial terms of defining equations and proves a conjecture on uniform bounds for divisors computing minimal log discrepancies.

Contribution

It provides a new characterization of semi-log canonical hypersurfaces and proves a conjecture on bounds for minimal log discrepancies in two dimensions.

Findings

Characterization of semi-log canonical hypersurfaces via initial equations

Proof of a conjecture on uniform bounds for divisors computing minimal log discrepancies

Results hold in arbitrary characteristic

Abstract

In this paper we characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an application, we prove a conjecture about a uniform bound of divisors computing minimal log discrepancies for two dimensional varieties, which is a conjecture by Ishii and also a special case of the conjecture by Musta\c{t}\v{a}-Nakamura.