Timeline for Sources for describing the characteristic polynomial of a nonintegral hyperplane arrangement in terms of point counting?
Current License: CC BY-SA 4.0
6 events
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| Sep 28, 2020 at 19:22 | history | edited | Will Dana | CC BY-SA 4.0 |
Added more specific variation on question to the end.
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| Sep 27, 2020 at 17:27 | comment | added | Richard Stanley | I would not call counting points over $\mathbb{F}_q$ "entirely combinatorial." This may be the case for hyperplanes like $x_i=\pm x_j$, where the arithmetic of finite fields is irrelevant, but once you have hyperplanes like $x_i+x_j+x_k=0$, then the counting will involve algebra. That is why, for instance, the number of regions of the resonance arrangement remains intractable. For nonintegral arrangements, the best tool seems to be Whitney's theorem. See for instance Sections 5 and 6 of www-math.mit.edu/~rstan/papers/deform.pdf. | |
| Sep 27, 2020 at 17:26 | comment | added | Sam Hopkins | Perhaps Theorem 9.1 of arxiv.org/abs/math/0309330, which is a general formula using the Möbius function for any valuation, is useful for you. | |
| S Sep 27, 2020 at 16:52 | history | suggested | RobPratt | CC BY-SA 4.0 |
corrected spelling in title
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| Sep 27, 2020 at 16:47 | review | Suggested edits | |||
| S Sep 27, 2020 at 16:52 | |||||
| Sep 27, 2020 at 16:45 | history | asked | Will Dana | CC BY-SA 4.0 |