Log Terminal Singularities

TL;DR

This paper introduces a new perspective on singularities of normal varieties by defining log terminal+ singularities and relating them to existing concepts through finite generation, advancing the understanding within the Minimal Model Program.

Contribution

It proposes a novel notion of discrepancy and log terminal+ singularities, connecting these with established log terminal singularities via finite generation techniques.

Findings

Defined a new discrepancy for normal varieties

Introduced log terminal+ singularities

Established relations with existing log terminal singularities

Abstract

In this paper we give a new point of view for optimizing the definitions related to the study of singularities of normal varieties, introduced in [dFH09] and further studied in [Urb12a] and [Urb12b], in relation to the Minimal Model Program. We introduce a notion of discrepancy for normal varieties, and we define log terminal+ singularities. We use finite generation to relate these new singularities with log terminal singularities (in the sense of [dFH09]).