Timeline for Extension of a first order deformation of a sheaf
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2011 at 11:37 | vote | accept | TonyS | ||
| Mar 15, 2011 at 9:01 | comment | added | Francesco Polizzi | (1) I assume that $[F]$ lies in the open set of the moduli space where the universal family exists. (2) You can assume that $C$ is a smooth and connected quasi-projective curve, in particular you can assume that it lies in one connected component of $M$. In fact, since $M$ is quasi-projective, you can obtain $M$ as a (general) complete intersection of hyperplane sections through $[F]$. | |
| Mar 14, 2011 at 19:43 | comment | added | TonyS | Okay, that looks good. Two questions: i thought a universal family only exists if $M$ is a fine moduli space? Or can we do this locally where such a family exists? What about connectedness of $C$? Can we always choose $C$ in such a way that we stay in one connected component of $M$? | |
| Mar 14, 2011 at 18:48 | history | answered | Francesco Polizzi | CC BY-SA 2.5 |