Timeline for Dimension of Hilbert scheme?
Current License: CC BY-SA 3.0
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| Oct 22, 2014 at 19:10 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Oct 22, 2014 at 18:52 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Oct 22, 2014 at 18:47 | comment | added | Francesco Polizzi | You are welcome. Note that in this way you show that the irreducible component of $\textrm{Hilb}(X)$ passing through $X$ is (generically) smooth of dimension $m$. I do not think that you can say anything about the connected component with your assumptions: the Hilbert scheme can be very pathological, and maybe some component of bigger dimension can intersect $\textrm{Hilb}_{[V]}(X)$ away from $[V]$. | |
| Oct 22, 2014 at 18:42 | comment | added | mark | Thanks a lot! I suspected this was OK, but worried I was missing some subtlety. | |
| Oct 22, 2014 at 18:41 | vote | accept | mark | ||
| Oct 22, 2014 at 18:30 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |