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Mar 30, 2022 at 11:41 comment added aiz89 @ Dori Bejleri: You're right I didn't define properly the log deformations I'm talking about. You're supposed to fix the log structure on the thickened base scheme in advance, and if you take the one which allows "smoothings", I think that one disallows the trivial deformation. Edited the question. (I'm still not sure I know what I'm talking about, but at least note that the general theorem about 1st order log deformations says "torsor" or something equivalent -- if the trivial deformation was allowed, it wouldn't say that).
Mar 30, 2022 at 11:34 history edited aiz89 CC BY-SA 4.0
(Edit) explained better the setup of the log deformation problem
Mar 30, 2022 at 3:44 comment added Dori Bejleri Why doesn't the image of $\psi$ contain $0$? I think the element $0$ should correspond to the trivial deformation and the trivial deformation of the log scheme $(C, M_C)$ maps to the trivial deformation of $C$ when you forget $M_C$.
S Mar 29, 2022 at 23:11 review First questions
Mar 29, 2022 at 23:27
S Mar 29, 2022 at 23:11 history asked aiz89 CC BY-SA 4.0