Timeline for Identifying elements in the kernel of an explicit endomorphism of a Jacobian variety
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2019 at 22:14 | comment | added | Michael Stoll | @EduardoR.Duarte If you send me an email, I can send you the code that does the computation. -- I think the reason why the expressions you got are so large is mainly that the coordinates coming from the Mumford representation are not very nice in a way, whereas the coordinates on the Kummer surface correspond to a full linear system. | |
| Mar 31, 2019 at 19:55 | comment | added | Eduardo R. Duarte | Prof, this is really nice, I just accepted the answer. I assume that $x_1,x_2, x_3,x_4$ are standard coordinates found in Prolegomena Flynn's book. I am really interested in the MAGMA computation in fact. Why the formulas are so small ? When I calculated $\sqrt{5}\in\text{End}(J)$ I used the generic point of $g\in J$ and then the action of $\zeta_1,\zeta_4\in\text{End}(J)$ in $g$. The final formulas are obtained through $2(\zeta_1(g)+\zeta_4(g))+g=\sqrt{5}(g)$. These formulas are huge. Yours are very compact, is there something I am missing? | |
| Mar 31, 2019 at 19:45 | vote | accept | Eduardo R. Duarte | ||
| Mar 30, 2019 at 10:01 | comment | added | Michael Stoll | @EduardoR.Duarte I have done the computation of the polynomials for the curve you mention and added the result to my answer. | |
| Mar 29, 2019 at 17:32 | history | edited | Michael Stoll | CC BY-SA 4.0 |
Added explicit polynomials for the special case mentioned in the comments.
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| Mar 28, 2019 at 16:23 | comment | added | Eduardo R. Duarte | One think to add is that I tried to do what you said of extending the function field resulting always in "out of memory" problems after some days. | |
| Mar 28, 2019 at 16:16 | comment | added | Eduardo R. Duarte | Prof. Stoll. Thanks for the answer. In fact I retook a problem, using also your advice from some time ago, which was to extend the function field of the jacobian to the denominators). My profile in mathoverflow changed since univ. mail does not exists anymore. Related to your answer, I would need then to calculate the endomorphism mapped to the Kummer Surface, in my case I have to map concretely $\sqrt{5}\in\text{End}(J)$ where $J$ is the Jacobian of $H:y^2=x^5 + 10$ over $\mathbb{Q}$. Any suggestions? (technically talking) do you know if someone has done this for explicit endomorphisms? | |
| Mar 24, 2019 at 19:05 | history | answered | Michael Stoll | CC BY-SA 4.0 |