Timeline for Classification of first order deformations of n-pointed non-singular variety
Current License: CC BY-SA 3.0
4 events
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| Mar 31, 2017 at 6:55 | comment | added | Will Chen | If instead of marking by points, we mark by a closed subscheme $D$ of positive dimension, then do you know if the deformations of the variety with marking by $D$ are still locally trivial? In my proof below of the local triviality of deformations of $X$ marked by a point, I used the fact that a point is etale over the base (Spec $k$) to identify $I/I^2$ with the module of differentials - I wonder if my proof could be adjusted to work for more general markings. | |
| Mar 28, 2017 at 4:03 | comment | added | Dan Petersen | @oxeimon Yes. The configuration space of ordered points is finite étale over the unordered configuration space, and formal étaleness identifies the 1st (or higher) order deformation problems. | |
| Mar 28, 2017 at 1:07 | comment | added | Will Chen | Are the 1st order deformations of an $n$-pointed (points are ordered) smooth variety the same as those when you consider the points to be unordered (ie, a divisor)? Intuitively, in the unordered case, infinitesimal automorphisms shouldn't be able to exchange points, so any infinitesimal automorphism which possibly only fixes the points as a set actually fixes them pointwise. I don't know how to formally argue this though... | |
| Feb 17, 2013 at 10:55 | history | answered | Dan Petersen | CC BY-SA 3.0 |