Characterization of two-dimensional semi-log canonical hypersurfaces 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.