references for singularities: does quotient singularities imply gorenstein? Is there a good place where to learn about singularities of algebraic varieties?
OK, this question is terribly vague, so I'll ask what I'm currently interested in: if X is a smooth variety and G is a finite group, then is $X/G$ Gorenstein? If true, what would a reference be?

The standard textbook references for learning singularities and their resolution are:


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*Greuel/Lossen/Shustin - Introduction to Singularities And Deformations, Springer 2007.

*Kollár, J. - Lectures on Resolution of Singularities, Princeton University Press 2007.

*Cutkosky, S. D. - Resolution of Singularities, AMS Graduate Studies in Mathematics 2004.

*Kollár/Kovács - Singularities of the Minimal Model Program, Springer 2013.

*Hauser et al. - Resolution of Singularities, a Research Textbook, Birkhauser 2000.


Specially, Kollár's and Cutkosky's are great books giving many examples and proving Hironaka's famous resolution theorem. Maybe you could find there the kind of topics you are interested in. For an introduction to singularities and a deeply conceptual overview towards such a theorem, there is the fantastic freely available article:


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*Hauser, H. - The Hironaka theorem on resolution of singularities (Or: a proof we always wanted to understand), Bulletin of the AMS vol. 40 no.3, p.323-403, 2003.

