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7
votes
1answer
343 views

Is there a way to check if a relative Hilbert Scheme is reduced?

More specifically, suppose I have a rational curve on a complete intersection, and I know that the relative Hilbert Scheme is not smooth at the point corresponding to my rational curve. Is there any ...
4
votes
1answer
319 views

What are the “special” strata of Sym^n(C^2)?

The affine variety $Sym^n(\mathbb{C}^2)$ has a natural quantization as a spherical rational Cherednik algebra. Thus, any primitive ideal of the rational Cherednik algebra has an corresponding ideal ...
1
vote
1answer
246 views

Request for info on the space of commuting matrices preserving a flag.

Fix a flag of subspaces V1 in V2 in V3, etc. all in Cn. Consider the space of pairs of commuting linear transformations A and B such that: A preserves the flag (i.e. A(Vi) is in Vi), and B strictly ...
7
votes
4answers
2k views

When are Hilbert schemes smooth?

I know that Hilbert schemes can be very singular. But are there any interesting and nontrivial Hilbert schemes that are smooth? Are there any necessary conditions or sufficient conditions for a ...