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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?

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    This is outside my area of knowledge, but [this paper](http://www.pitt.edu/~borisov/Documents/papers/quot_fact_RH.pdf) discusses a procedure for modifying a quotient singularity that is not Gorenstein to a different quotient singularity that is Gorenstein. So I presume, based on context, that the answer to your question is no, though I don't know a counterexample myself. However, I thought I would mention this in case the technique of the paper is helpful to you.2012-04-25
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    ah, interesting. I had never heard of a gorenstein index before. Is this definition of gorenstein the same as the usual one? (also, of being gorenstein I only need the dualising complex to be a bundle)2012-04-25

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