Timeline for Can we define Whitney stratification algebraically?
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11 events
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| Sep 6, 2022 at 16:31 | answer | added | Vidit Nanda | timeline score: 12 | |
| Jan 16, 2022 at 3:24 | comment | added | Geordie Williamson | @Z.M Yes, my understanding is that ULA is precisely this: vanishing of vanishing cycles in any direction. However this seems somewhat tautological to me. I'd be interested if there is a more cumulative algebra criterion, but perhaps this is unrealistic. | |
| Jan 13, 2022 at 11:28 | comment | added | Con | I think Theorem 6.6 of arxiv.org/pdf/1109.5886.pdf might be of interest to you. The author also shows that these "$t$-stratifications" induce Whitney stratifications. | |
| Jan 13, 2022 at 7:21 | comment | added | Z. M | @GeordieWilliamson I am a layman, but do universal local acyclicity maps work like that? | |
| Jan 13, 2022 at 3:34 | answer | added | Balarka Sen | timeline score: 2 | |
| Jan 13, 2022 at 1:49 | comment | added | UVIR | @TomGoodwillie Given an algebraic variety, we can consider the set of its smooth points. Then for the set of singular points (which has strictly lower dimension) we can consider its set of smooth points again. This construction gives a stratification which is algebraic but not necessarily Whitney. | |
| Jan 13, 2022 at 1:42 | comment | added | Geordie Williamson | A closely related question that I've often wondered about: is it possible to define "topologically locally trivial fibration" in commutative algebra? Of course "smooth morphism" covers smooth fibres, but when the fibres are singular I'm not sure... | |
| Jan 13, 2022 at 1:39 | comment | added | Geordie Williamson | @TomGoodwillie a classic example is given by Whitney's umbrella: the stratification by "regular locus" union "singular locus" is not Whitney. | |
| Jan 12, 2022 at 21:50 | comment | added | Tom Goodwillie | Do you have in mind an example of a non-Whitney but algebraic stratification of something? | |
| Jan 12, 2022 at 19:53 | history | edited | LSpice | CC BY-SA 4.0 |
Typo in title
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| Jan 12, 2022 at 19:43 | history | asked | UVIR | CC BY-SA 4.0 |