Timeline for Counting the number of poles for rational functions in a coordinate ring of a curve
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2019 at 13:18 | comment | added | Felipe | Dear @Will Sawin. I'm still thinking about this proof. Do you have some step by step proof of this result? Thank you! | |
| Dec 29, 2018 at 20:32 | vote | accept | Felipe | ||
| Dec 29, 2018 at 20:23 | comment | added | Will Sawin | @Felipe Yes, that's the point. The main difficulty in this question is translating between the different languages used and interpreting the references, which is not basic, but once the language is understood it's pretty basic. I would imagine that a version of this argument is somewhere in the first chapter or the Riemann-Hurwitz section of the curves chapter of Hartshorne, but I don't know. | |
| Dec 29, 2018 at 20:15 | comment | added | Felipe | One more question. For example, considering the case when $u^2=t^2-2bt+1$, with $b\in\mathbb{C}\setminus\{\pm 1\}$. It is well known that the ring $\mathbb{C}[t,t^{-1},u]/\langle u^2=t^2-2bt+1 \rangle$ has 4 points removed. Using your formula we will have that $n=\gcd(2,0)+\gcd(2,2)=2+2= 4$. That's the point? | |
| Dec 29, 2018 at 20:05 | comment | added | Felipe | Thank you @Will Sawin. Could you please give some references that this argument appear? Furthermore, would you rate this question as a very basic question in algebraic geometry? | |
| Dec 29, 2018 at 19:51 | history | answered | Will Sawin | CC BY-SA 4.0 |