Timeline for Characterization of an Abelian surface
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2021 at 8:17 | comment | added | Yuan Yang | @JonathanLove For non-closeness of Q: if the variety base change to $\bar{Q}$ is an abelian variety, then either: it doesn’t have a rational point; or it’s an abelian variety over Q, too. | |
| Dec 1, 2021 at 8:02 | comment | added | Yuan Yang | @JonathanLove My current status is: I have an algebraic surface in $P^1*P^1*P^1*P^1$, and I have families of elliptic curves(I actually have $P^1$ families of them), but for each family, these curves are not disjoint-they actually all intersect in one point, at one of the infinity point. But indeed, any two family intersect at only one point. | |
| Dec 1, 2021 at 7:52 | vote | accept | Yuan Yang | ||
| Dec 1, 2021 at 7:52 | comment | added | Yuan Yang | @JonathanLove Yes indeed. I‘ve made quite a few mistakes. It's more complicated than I thought. | |
| Dec 1, 2021 at 1:49 | comment | added | Jonathan Love | @Yuan It sounds like your application might involve considering varieties defined over $\mathbb{Q}$? The solution afh gives here depends quite heavily on the algebraically closed assumption - there are a lot of subtleties that arise if you're trying to work over number fields (even the problem statement, as it's currently given, isn't well-posed). | |
| Nov 30, 2021 at 2:02 | comment | added | Yuan Yang | I think we just solved the 'four-distance' problem using this result. Although I don't know whether or not it is solved yet. Can we talk by email? Please contact me at [email protected] | |
| Nov 30, 2021 at 1:59 | history | edited | afh | CC BY-SA 4.0 |
added 6 characters in body
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| Nov 30, 2021 at 1:41 | history | edited | afh | CC BY-SA 4.0 |
edited body
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| Nov 30, 2021 at 1:32 | history | answered | afh | CC BY-SA 4.0 |