Timeline for A question on infinitesimal deformation (related to intersection theory)
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Mar 1, 2014 at 22:52 | history | bounty ended | CommunityBot | ||
| S Mar 1, 2014 at 22:52 | history | notice removed | CommunityBot | ||
| Feb 22, 2014 at 2:39 | comment | added | Vladimir Baranovsky | Ok, if you say that the tangent spaces are $H^0(\mathcal{N}_{Z|\mathbb{P}^n})$ then you are deforming $Z$ and $Z'$ as subschemes of $\mathbb{P}^n$ not of $X$, as I misunderstood. Then taking the $m$-power of the deforming ideal does not quite work. | |
| S Feb 21, 2014 at 21:21 | history | bounty started | user46578 | ||
| S Feb 21, 2014 at 21:21 | history | notice added | user46578 | Draw attention | |
| Feb 21, 2014 at 18:21 | comment | added | user46578 | @Baranovsky: May be I am getting this wrong. $X \otimes Spec(k[\epsilon]/(\epsilon^2)$ is not a first order deformation of $X$. May be you meant $X \times Spec(k[\epsilon]/(\epsilon^2)$ which is the trivial deformation. It is also not guarenteed that a first deformation of $Z$ comes from a first order deformation of $X$. Could you elaborate on your argument a bit more? | |
| Feb 21, 2014 at 18:10 | comment | added | Vladimir Baranovsky | If your first order deformation of $Z$ is a subscheme of $X \otimes Spec (k[\varepsilon]/\varepsilon^2)$ with ideal sheaf $J$ then it seems that $J^m$ will define a subscheme deforming $Z'$. Unless I misunderstood the question. | |
| Feb 21, 2014 at 18:01 | comment | added | user46578 | @Baranovsky: I do not understand the question. "What happens" is a very broad question. Is there any specific property you are inquisitive about? | |
| Feb 20, 2014 at 21:52 | comment | added | Vladimir Baranovsky | If your deformation of Z is a subscheme with ideal sheaf J, what happens when you consider the ideal J^m? | |
| Feb 19, 2014 at 21:14 | history | asked | user46578 | CC BY-SA 3.0 |