Timeline for Kodaira-Spencer map in a concrete instance
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2010 at 18:18 | comment | added | Qfwfq | Actually, I was trying genus 2, in which case $H^0(X,K_X^2)=S^2H^0(X,K_X)$, so you can use the (tensor products of pairs of elements of the) base I indicated. | |
| Apr 24, 2010 at 18:14 | comment | added | Qfwfq | Haha! ;) No, that was just a misprint! I've edited now. | |
| Apr 24, 2010 at 3:48 | comment | added | Sasha | I guess the problem with the computation may be due to the fact that the dual of $H^1(X,T_X)$ is NOT $H^0(X,K_X)$, BUT $H^0(X,2K_X)$! | |
| Apr 23, 2010 at 15:48 | comment | added | Qfwfq | I was trying to compute the cocycle in H^1(X,T_X) as explained, e.g., in the book by Claire Voisin. You cover the (total space of the family) with affine open sets $V$ so small that you have an isomorphism between each of them and a cartesian product $V_{red}\times \Delta$, then the epsilon components of the "transition functions" give derivations on the coordinate rings of the double intersections: that's the Cech cocycle. - The problem is that it's not obvious (to me) what this trivializing open affines should be in this simple concrete case. | |
| Apr 23, 2010 at 14:50 | history | answered | Kevin H. Lin | CC BY-SA 2.5 |