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Compound Du Val 3-fold singularities form a good class of singularities in 3-fold singularity theory. I would like to know which singularities admit crepant resolutions. If I remember correctly, $cA_{n}$ admits a crepant resolution. What about $cD_{n}$- and $cE_{n}$-singularities?

I would really appreciate it if you could give me a reference or explain what is known about crepant resolution of cDV singularities.

Thank you for your help.

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What's a compound du val singularity? Bridgeland-King-Reid have a paper treated 3-fold quotient singularities by finite subgroups of SL(3). I assume that's Du Val singularity for 3-folds? – temp Sep 19 '12 at 5:19
It does not seem possible to say that $cA_n$ admits a crepant resolution. For example, $x^2+y^2+z^2+t^n=0$ is $cA_1$ for $n\ge 2$ but has a crepant resolution if and only if $n$ is even. – inkspot Sep 19 '12 at 10:11
For an answer in the $cA_n$ case see Katz's paper: "Small resolutions of Gorenstein threefold" (small is equivalent to crepant in this case) . The $cD_n$ case seems a lot harder, it was discussed a bot there also, but I do not know any other references. – Hailong Dao Sep 19 '12 at 18:03

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