Timeline for Distribution of rational points in the real locus of a planar algebraic curve
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 6, 2020 at 12:18 | comment | added | user158636 | @StanleyYaoXiao yes, you are right. I didn't mean that in a statistical sense necessarily, just that there is finitely many unordered tuples of non-negative integers so one can ask which are realizable. | |
| Aug 6, 2020 at 12:08 | comment | added | Stanley Yao Xiao | It is likely that the average number of rational points on curves of genus 3 is zero, so it is very hard to talk about a "distribution" in such a setting. On average, each component will have no rational points. | |
| Aug 6, 2020 at 1:53 | comment | added | JSE | Also, taking P_0 to be a basepoint, I believe you can tell which component you're on by looking at the class of P - P_0 in J(Q) / 2J(Q). | |
| Aug 6, 2020 at 1:52 | comment | added | JSE | I don't know the answer to this question, but the Bombieri-Pila/Heath-Brown method suggests that low-height points like to repel each other p-adically (including oo-adically) so one might imagine that, statistically speaking, the lowest-height points would be biased towards lying on different components | |
| Aug 6, 2020 at 1:09 | history | asked | user158636 | CC BY-SA 4.0 |