Timeline for Rational surface singularities as Toric varieties
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2013 at 15:55 | comment | added | Allen Knutson | If you puncture ${\mathbb C}^2$, you get something that retracts to $S^3$, a simply-connected space on which $\Gamma$ acts without fixed points. As for the toric side, when the edges coming out of a vertex are a $\mathbb Q$-basis, and so generate a subgroup of ${\mathbb Z}^n$ with finite cokernel $\Gamma^*$, a neighborhood of the point is isomorphic to ${\mathbb A}^n / \Gamma$. I think this is in [Fulton, Intro to TVs] under "rational smoothness". | |
| Oct 23, 2013 at 15:48 | comment | added | Allen Knutson | The groups are here: en.wikipedia.org/wiki/… | |
| Oct 23, 2013 at 12:04 | comment | added | Katie Dobbs | I am not very familiar with this material. Do you mind giving me some extra details? Specifically I would like to know what the $\Gamma$ are, why $\Gamma$ is the $\pi_1$ of a punctured nbhd of the singular point and why for punctured nbhds of toric surface singularities $\pi$ must be abelian (I realised this list is everything you said unfortunately :( ). I realise I'm asking a lot, I'd be grateful if you could point me to some references for those facts if you don't want to type up the details. Thank you for your help! EDIT: I can probably find a list of the $\Gamma$ on my own actually. | |
| Oct 23, 2013 at 11:11 | history | answered | Allen Knutson | CC BY-SA 3.0 |