Timeline for Resolving quotient singularities without the quotient
Current License: CC BY-SA 3.0
5 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Feb 21, 2016 at 21:57 | comment | added | Lev Borisov | The problem with taking a crepant resolution and then normalization is that the result will typically be singular. | |
| Feb 21, 2016 at 15:56 | comment | added | Jason Starr | In the quasi-projective case, every birational, projective morphism can be obtained as a blowing up. However, there is no guarantee that the ideal sheaf will be equivariant, nor that the corresponding closed subscheme will have support strictly contained in the fundamental locus of the birational morphism. | |
| Feb 21, 2016 at 15:38 | comment | added | Will Sawin | You can start with a crepant resolution, that is a smooth variety with a $G$-torsor over an open subset. You can take $\tilde{X}$ to be the normalization of that $G$-torsor over the crepant resolution. Then its quotient by $G$ will certainly be the crepant resolution. However I don't know whether this normalization can always be obtained by blowing up. | |
| Feb 21, 2016 at 14:58 | history | asked | Alex | CC BY-SA 3.0 |