Singularities on normal varieties

TL;DR

This paper extends the theory of singularities of pairs and multiplier ideal sheaves to arbitrary normal varieties, removing previous restrictions like Q-Gorenstein conditions, thus broadening the scope of the existing framework.

Contribution

It generalizes the definitions and properties of singularities of pairs and multiplier ideals to all normal varieties, regardless of Q-Gorenstein assumptions.

Findings

Definitions extend naturally to arbitrary normal varieties

Main features of the theory are preserved in this general setting

Framework now applicable to a wider class of algebraic varieties

Abstract

In this paper we generalize the definitions of singularities of pairs and multiplier ideal sheaves to pairs on arbitrary normal varieties, without any assumption on the variety being Q-Gorenstein or the pair being log Q-Gorenstein. The main features of the theory extend to this setting in a natural way.