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

Some properties and examples of log terminal+ singularities