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I am looking for some references on equivariant resolution of singularities. In most references quoted on mathoverflow (for instance : Reference on an equivariant resolution of singularities), they only talk about finite group action (if I am not mistaken).

I was wondering if it is known that equivariant resolutions do not exist in general for larger group (are there counter-examples?). I am especially interested when the group is $\mathbb{C}^*$.

Thanks in advance.

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    $\begingroup$ Equivariant resolutions exist for the action of any algebraic group. See, for example, 3.9.1 in Kollar's book "Lectures on resolution of singularities". $\endgroup$ – ulrich Sep 26 '13 at 10:58
  • $\begingroup$ @ulrich Thanks! I still wonder why many papers only deal with finite group actions. But that does not really matter, now I have this reference. $\endgroup$ – Libli Sep 26 '13 at 12:10
  • $\begingroup$ I've need to reference this in a paper and used: Cor 7.6.3, O. E. Villamayor U. Patching local uniformizations. Ann. Sci. E ́cole Norm. Sup. (4), 25(6):629–677, 1992. $\endgroup$ – Jim Bryan Sep 26 '13 at 18:00

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