Timeline for Dimension of the Hilbert scheme of curves
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2012 at 11:32 | comment | added | Alex | I am interested in general $g,n,r$, for generic $C$ their values are restricted by the Brill-Noether number being nonnegative. | |
| Jul 19, 2012 at 20:05 | comment | added | Jason Starr | @Alex: "I am mainly interested in smooth $C$". Are you interested in "general" or "generic" $C$? If so, then Brill-Noether theory essentially gives a complete answer. | |
| Jul 19, 2012 at 16:05 | comment | added | Alex | I am aware of this inequality. I wonder if something more precise is known (or at least conjectured). I am mainly interested in smooth $C$. | |
| Jul 19, 2012 at 14:36 | comment | added | Francesco Polizzi | You are right. I corrected the answer, thank you. | |
| Jul 19, 2012 at 14:35 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Jul 19, 2012 at 14:24 | comment | added | Jason Starr | The dimension inequality you write is true if $C$ is a local complete intersection scheme. In general, you do need some extra conditions to reduce the "natural" obstruction group to $H^1(C,\mathcal{N})$, cf. pp. 33-35 of Koll\'ar's "Rational Curves on Algebraic Varieties". | |
| Jul 19, 2012 at 14:12 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Jul 19, 2012 at 13:59 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |