Timeline for Singularities of Hilbert scheme of points on a surface
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Dec 11, 2012 at 18:23 | comment | added | HNuer | I don't know of a general statement for $S^{[2]}$, but I know that in the simple case of, say, a surface with one node, the singular locus of $S^{[2]}$ is known. I don't remember the details precisely, but I believe it looks locally like $S\times C$, where $C$ is the smooth plane conic $S$ induces (alternatively the exceptional divisor of the blow-up of $S$ at the node). Less geometrically, the singular locus as one might expect consists of length 2 subschemes which are support at least partially at the node. It would probably not be too hard to generalize this to any nodal surface. | |
| Sep 27, 2010 at 21:30 | comment | added | Andrea Ferretti | Can you explain what is known in the normal case? It would already be interesting. | |
| Sep 27, 2010 at 16:30 | comment | added | Vivek Shende | I think it would be fair to say that no-one knows the answer even for curves. However if you are satisfied to assume $S$ is normal, the situation is much better. | |
| Mar 26, 2010 at 12:02 | history | asked | Andrea Ferretti | CC BY-SA 2.5 |