Timeline for Deformations of quotient singularities
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2014 at 16:10 | vote | accept | Puzzled | ||
| Feb 4, 2014 at 7:00 | history | edited | Francesco Polizzi |
edited tags
|
|
| Feb 3, 2014 at 21:46 | answer | added | Francesco Polizzi | timeline score: 2 | |
| Feb 3, 2014 at 20:04 | comment | added | Will Sawin | I should have said that locally somewhere it looks like that, not locally everywhere. | |
| Feb 3, 2014 at 19:52 | comment | added | Jason Starr | @WillSawin: "A codimension two finite quotient singularity ... has to locally look like ..." I believe this is incorrect. For instance, let the Klein Viergruppe, $V=(\mathbb{Z}/2\mathbb{Z})^3/\Delta(\mathbb{Z}/2\mathbb{Z})$ act on $\mathbb{A}^3$ by $\overline{e}_1(x_1,x_2,x_3) = (x_1,-x_2,-x_3)$, and similarly for $\overline{e}_2$ and $\overline{e}_3$. The quotient is the hypersurface in $\mathbb{A}^4$ of points $(y_1,y_2,y_3,z)$ such that $y_1y_2y_3-z^2 = 0$, where $y_i = x_i^2$ and $z = x_1x_2x_3$. This germ is not smooth over a two-dimensional germ. | |
| Feb 3, 2014 at 19:08 | comment | added | Will Sawin | I think that is a non-stupid example. A codimension two finite quotient singularity in dimension $3$ has to locally look like $\mathbb A^1 \times X$ for $X$ a finite quotient singularity in dimension $2$. | |
| Feb 3, 2014 at 18:57 | comment | added | abx | For your first question,a stupid example is $\mathbb{A}^1\times Q$, where $Q$ is a quadric cone in $\mathbb{A}^3$. | |
| Feb 3, 2014 at 18:52 | history | asked | Puzzled | CC BY-SA 3.0 |