Timeline for When do blow-up and quotient commute?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2012 at 7:12 | comment | added | Atsushi Kanazawa | The Kummer case is precisely Jerome's $SL(2,\mathbb{C})$ example, I think. | |
| Aug 31, 2012 at 4:40 | answer | added | Sasha | timeline score: 5 | |
| Aug 31, 2012 at 0:12 | comment | added | Will Sawin | For each affine of $X$, you can take the Spec of the integral closure of the coordinate ring in $\mathbb C(x_1, \dots, x_n)$ and glue together. I'm not sure when this is smooth, a blow-up, etc. | |
| Aug 30, 2012 at 22:22 | comment | added | Piotr Achinger | An obvious idea is take $Y$ to be a blowup of the fixed point set (or the set where $G$ does not act freely). I think this works for Kummer surfaces: if $A$ is an abelian surface then its Kummer surface $X$ is a crepant resolution of $A/i$ ($i$ is the involution $x\mapsto -x$ on $A$), but can also be described as $B/i$ where $B$ is the blowup of $A$ along the $2$-torsion subgroup (i.e. fixed points of $i$). | |
| Aug 30, 2012 at 21:48 | history | asked | Jerome | CC BY-SA 3.0 |