Timeline for Cohomology of tangent sheaf of a hypersurface
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 8, 2019 at 15:52 | vote | accept | CommunityBot | ||
| Mar 5, 2019 at 23:08 | comment | added | Enrico | An addendum: this nice paper by Sernesi (arxiv.org/pdf/1306.3736.pdf) gives informations on how to control the deformations of a singular reduced hypersurface in terms of the local cohomology of the cokernel that Sasha was mentioning. | |
| Mar 5, 2019 at 19:31 | comment | added | Sasha | This is right (I missed the absence of the smoothness assumption in the question). In the singular case the first sequence is not exact in the right term, but its cokernel is not so hard to control. It is isomorphic to $\mathcal{O}_Z(d)$, where $Z \subset \mathbb{P}^n$ is the subscheme defined by $\{ \partial F/\partial x_0 = \partial F/\partial x_1 = \dots \partial F/\partial x_n = 0 \}$, where $F$ is the equation of $X$. | |
| Mar 5, 2019 at 18:57 | comment | added | user125056 | I think that the first exact sequence you wrote holds only if $X$ is smooth. What if $X$ is singular? | |
| Mar 5, 2019 at 18:14 | history | answered | Sasha | CC BY-SA 4.0 |