Timeline for When do infinitesimal deformations lift to global deformations?
Current License: CC BY-SA 3.0
4 events
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| Feb 16, 2012 at 20:41 | comment | added | Paul | OK, my use of "$x^2$" was confusing, since it also arises in $k[x]/(x^2)$, or equivalently in taking the linearization $df$. I should have used $f(x)=x^3$! | |
| Feb 16, 2012 at 18:36 | comment | added | Matt | Oh I see what you're doing now. I was being dumb. The ker df should have tipped me off. I was very confused at what some ambient space was doing. I usually call what you described an "embedded deformation" (maybe this is not standard?). To me an infinitesimal deformation of $X_0/k$ is a flat map $X\to Spec (k[x]/(x^2))$ with special fiber $X_0$. Hartshorne defines global deformation to be any flat map $X\to T$ where some fiber $X_t\simeq X_0$. My guess is that Naga wants specific conditions on T (integral?), otherwise every infinitesimal is global. | |
| Feb 16, 2012 at 14:44 | history | edited | Paul | CC BY-SA 3.0 |
added 15 characters in body
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| Feb 16, 2012 at 14:37 | history | answered | Paul | CC BY-SA 3.0 |