Timeline for A question about relative deformations of the structure sheaf of the diagonal
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2021 at 16:51 | comment | added | Jon Pridham | I meant as a sheaf of DGLAs on $X$, since those also govern the local deformation problems. That DGLA doesn't live in $QCoh(X)$, as the Gerstenhaber bracket isn't $O_X$-bilinear. | |
| Apr 21, 2021 at 14:11 | comment | added | Grisha Konovalov | @JonPridham Thanks for another useful reference! May I ask for a clarification of your last point: literally, DGLA that controls deformations of the associative algebra $O_X$ is a DGLA in $\text{Vect}_\mathbb{C}$, not in $\text{QCoh}(X)$. Or you mean that one should argue about push-forward of my DGLA to point first? | |
| Apr 20, 2021 at 11:33 | comment | added | Jon Pridham | Also see Negron-Schedler arxiv.org/abs/1809.08715. Your intuition that the underlying dg Lie algebra should be homotopy abelian is correct though, as it's the loop space of the DGLA deforming $O_X$ as an associative algebra. | |
| Apr 20, 2021 at 9:59 | comment | added | Grisha Konovalov | @JonPridham Thanks a lot for commenting. As far as I understand, on the RHS, one has to multiply the isomorphism with smth similar to the Todd class of the tangent bundle to the power of -1/2. I will try to think through it. | |
| Apr 19, 2021 at 19:00 | comment | added | Jon Pridham | It's a bit more subtle than that. See e.g. Corollary 1.5 of Calaque-van den Bergh arXiv.org/abs/0708.2725. | |
| Apr 19, 2021 at 16:57 | review | First posts | |||
| Apr 19, 2021 at 17:07 | |||||
| Apr 19, 2021 at 16:19 | history | asked | Grisha Konovalov | CC BY-SA 4.0 |