Deformations of log terminal and semi log canonical singularities

TL;DR

This paper proves that certain mild singularities in algebraic geometry, specifically klt and slc singularities, remain stable under deformations when specific conditions are met, extending previous results in the field.

Contribution

It generalizes known invariance results of klt and slc singularities under deformations to broader conditions involving $Q$-Gorenstein fibers.

Findings

klt singularities are deformation invariant under $Q$-Gorenstein conditions

slc singularities also exhibit invariance under similar conditions

extends results of Esnault-Viehweg and S. Ishii

Abstract

In this paper, we prove that klt singularities are invariant under deformations if the generic fiber is $\mathbb{Q}$-Gorenstein. We also obtain a similar result for slc singularities. These are generalizations of results of Esnault-Viehweg and S. Ishii.