Some properties and examples of log terminal+ singularities

TL;DR

This paper explores the properties of log terminal+ (lt+) singularities, demonstrating their well-behaved nature and relationships to rational singularities, while providing examples illustrating potential pathologies in non-Q-Gorenstein cases.

Contribution

It introduces and studies the lt+ class of singularities, establishing key properties like Bertini, inversion of adjunction, and deformation invariance, and relates them to rational singularities.

Findings

lt+ singularities satisfy Bertini type results

Inversion of adjunction holds for lt+ singularities

Examples show possible pathologies in non-Q-Gorenstein cases

Abstract

In "Singularities on Normal Varieties", de Fernex and Hacon started the study of singularities on non-Q-Gorenstein varieties using pullbacks of Weil divisors. In "Log Terminal Singularities", the author of this paper and Urbinati introduce a new class of singularities, called log terminal+, or simply lt+, which they prove is rather well behaved. In this paper we will continue the study of lt+ singularities, and we will show that they satisfy a Bertini type result, inversion of adjunction and small deformation invariance, and that they are naturally related to rational singularities. Finally, we will provide a list of example (all of them with lt+ singularities) of the pathologies that can occur in the study of non-Q-Gorenstein singularities.