Timeline for Sheaf of differential and its reflexive hull on a toric variety
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 24, 2010 at 16:06 | comment | added | Sándor Kovács | I was going to say (after your first comment) that you need $Ext$ and not the cohomology of $\Omega$, which is a trivial comment, but explains why I asked what I asked in the answer... | |
| Nov 24, 2010 at 15:37 | comment | added | Zhiyu | It seems like there is an upper bound on how many words one can use in a comment. Let me explain a little more. Basically I need an isomorphism between $H^i(Ext(\Omega_D, \mathcal{O}_D)$ to $H^{i+2}(Hom(\Omega_D, \mathcal{O}_D))$. One way to do this is to try to relate these to the ambient weighted projective space. | |
| Nov 24, 2010 at 15:17 | comment | added | Zhiyu | Well, it is kind of a long story why I am interested in $\Omega_X$ rather than its reflexsive hull. Roughly speaking because the deformation theory is controlled by $\Omega_X$. I am trying to understand the deformation of a pair $(X, D)$. A question I asked a few days ago is here: mathoverflow.net/questions/45343/… The divisor $D$ is isomorphic to a (rather singular, but normal) weighted hypersurface in a weighted projective space. (But $X$ is not the weighted projective space!) So I am trying to relate the cohomology of D to the w.p.s. | |
| Nov 24, 2010 at 9:23 | history | answered | Sándor Kovács | CC BY-SA 2.5 |