Timeline for Two rings...are they isomorphic?
Current License: CC BY-SA 3.0
19 events
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| Nov 12, 2014 at 14:30 | history | edited | KConrad | CC BY-SA 3.0 |
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| Nov 12, 2014 at 14:08 | vote | accept | Nicholas Proudfoot | ||
| Nov 12, 2014 at 14:08 | history | edited | Nicholas Proudfoot | CC BY-SA 3.0 |
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| Nov 12, 2014 at 8:59 | comment | added | Mariano Suárez-Álvarez | @NicholasProudfoot, please do revert the edit and ask another question. | |
| Nov 12, 2014 at 8:54 | comment | added | Francesco Polizzi | I completely agree with Vladimir Dotsenko. | |
| Nov 12, 2014 at 8:03 | comment | added | Vladimir Dotsenko | It would be extremely helpful to roll back the edit, accept Bjorn's answer, and create a separate question for the new pair of rings. The way it is done now makes Bjorn's answer hanging there without any context, it is very misleading. | |
| Nov 12, 2014 at 5:09 | comment | added | Nicholas Proudfoot | Since I've already made the edit, I'm going to let it stand, but I promise not to change the problem again! | |
| Nov 12, 2014 at 4:40 | comment | added | Nicholas Proudfoot | @Joe Silverman: Thanks, that was a typo! I meant to leave t out of the main question. | |
| Nov 12, 2014 at 4:39 | history | edited | Nicholas Proudfoot | CC BY-SA 3.0 |
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| Nov 12, 2014 at 4:36 | comment | added | Joe Silverman | You might want to say what $t$ is. (You mentioned it in your comment to Bjorn's answer, but it really needs to be in the statement of your question. I originally assumed it was a new variable.) | |
| Nov 12, 2014 at 4:23 | history | edited | Nicholas Proudfoot | CC BY-SA 3.0 |
My original question was too simple to capture the spirit of the examples I want to understand (as Bjorn Poonen demonstrated).
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| Nov 12, 2014 at 4:17 | comment | added | Nicholas Proudfoot | Given a hyperplane arrangement A, one can associate a certain variety X(A), called the "reciprocal plane" of A. This variety has a stratification by flats F of A. The closure of the F-stratum is isomorphic to X(A_F) (the localized arrangement). I want it to be the case that this stratum has a normal slice isomorphic to X(A^F) (the restricted arrangement), at least formally. I can produce a normal slice, but rather than obtaining X(A^F), I'm obtaining a deformation thereof. I'm hoping that this deformation is isomorphic to X(A^F), at least in a formal neighborhood of the origin. | |
| Nov 12, 2014 at 3:57 | comment | added | KConrad | Nick, out of curiosity, what was leading you to a different answer than what you expected? | |
| Nov 12, 2014 at 3:37 | comment | added | Nicholas Proudfoot | Both rings become isomorphic after passing to the associated graded of the filtration by powers of the maximal ideal. Geometrically, this is the statement that Spec(R) and Spec(S) have isomorphic tangent cones (at their unique closed points). | |
| Nov 12, 2014 at 3:34 | answer | added | Bjorn Poonen | timeline score: 18 | |
| Nov 12, 2014 at 3:21 | comment | added | Daniel Litt | What's the dimension of $\mathfrak{m}^3/\mathfrak{m}^4$ in both cases? Not an answer, just the first thing I'd try. | |
| S Nov 12, 2014 at 2:44 | history | suggested | gaoxinge | CC BY-SA 3.0 |
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| Nov 12, 2014 at 2:38 | review | Suggested edits | |||
| S Nov 12, 2014 at 2:44 | |||||
| Nov 12, 2014 at 2:23 | history | asked | Nicholas Proudfoot | CC BY-SA 3.0 |