Timeline for Reference request: is the punctual Hilbert scheme irreducible?
Current License: CC BY-SA 2.5
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| Jun 6, 2010 at 18:02 | comment | added | George McNinch | Probably the OP was interested (only?) in char. 0, which is the case treated by Briancon. Tony Iarrobino [Punctual Hilbert schemes. Mem. Amer. Math. Soc. 10 (1977)] proved the irreducibility in char p>0 for d = 2 and p>n. More recently, Sasha Premet proved this irreducibilty (for d=2) for all alg. closed fields [Nilpotent commuting varieties of reductive Lie algebras. Invent. Math. 154 (2003)]; his argument uses an observation of of Baranovskiĭ (relating the "nilpotent commuting variety" with the punctual Hilbert scheme). Premet's approach seems to be a simplification already in char. 0. | |
| Apr 8, 2010 at 9:56 | history | answered | MartinG | CC BY-SA 2.5 |