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.

  • 3
    $\begingroup$ 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

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.