Timeline for Effective bound on "Jacobian rank" for (regular) planar algebraic curves
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2023 at 12:08 | comment | added | Loïc Teyssier | Let me reflect a little bit more about this, and I'll accept your answer. | |
| Apr 17, 2023 at 12:07 | comment | added | Loïc Teyssier | Your mention of the Nullstellensatz is spot-on, since in the case of a regular curve $f$ and its partial derivatives have no common zero, hence the Nullstellensatz provides polynomials $A,B,C$ such that $\phi(A,B,C)=1$, at which point $\phi$ has maximal rank (modulo a shift on the degree of its arguments, but that's probably ok for my purposes). The effective version you point to in your answer provides a sharp a priori bound on the degree of $A,B,C$. | |
| Apr 15, 2023 at 22:27 | comment | added | Jorge Vitório Pereira | You are welcome. Hope this help, even if I am not sure it is actually relevant for your question. At a first quick reading, I though that you were looking for bounds like the one in effective Nullstelensatz. Sorry about that. Anyway, you may also want to take a look in a recent preprint by Camacho and Movasati where they address the problem of generation of the module of vector fields tangent to a mildly singular curve algorithmically. | |
| Apr 15, 2023 at 20:52 | comment | added | Loïc Teyssier | Thanks a lot Jorge, I'll have a look at all this. | |
| Apr 15, 2023 at 16:49 | history | edited | Jorge Vitório Pereira | CC BY-SA 4.0 |
I misread the question. Edited the answer accordingly.
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| Apr 15, 2023 at 16:37 | history | answered | Jorge Vitório Pereira | CC BY-SA 4.0 |