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Some Properties and Examples of Log Terminal+ Singularities

In [6], de Fernex and Hacon started the study of singularities on non-ℚ-Gorenstein varieties using pullbacks of Weil divisors. In [4], the author of this article and Urbinati introduce a new class of singularities, called log terminal+, or simply lt+, which they prove is rather well behaved. In this article we will continue the study of lt+ singularities, and we will show that they can be detected by a multiplier ideal, 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 examples (all of them with lt+ singularities) of the pathologies that can occur in the study of non-ℚ-Gorenstein singularities.