Timeline for Dimension of Prym variety of cover
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2020 at 16:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 29, 2020 at 19:54 | answer | added | Doug Liu | timeline score: 2 | |
| Jun 28, 2019 at 17:03 | comment | added | 57Jimmy | @StanleyYaoXiao Thanks for the explanation, but it's still not completely clear to me: by Riemann-Hurwitz, the number of points in the ramified fiber determines the genus, so what do you mean by "this can always be done"? Here we consider all Aff(q)-covers branched at a single point, so also those that have more than one point in the fiber, and then take a non-Galois subcover of order $q$ by quotienting $\mathbb{F}_q^*$, right? | |
| Jun 28, 2019 at 16:54 | comment | added | Stanley Yao Xiao | I don't think that's the reason... they constructed the covers to have only one point of ramification. This can always be done, by the work of Fulton (see: jstor.org/stable/1970748?seq=1#page_scan_tab_contents) | |
| Jun 28, 2019 at 16:51 | comment | added | 57Jimmy | @StanleyYaoXiao Thanks for the remark! But why can I only have one element in the ramified fiber? Is it because $q$ is prime? But the cover $C_1' \to C_2$ is not Galois, even away from the ramification... | |
| Jun 28, 2019 at 16:39 | comment | added | Stanley Yao Xiao | Check the ramification index $e_P$ at the (only) point of ramification | |
| Jun 28, 2019 at 15:05 | review | First posts | |||
| Jun 28, 2019 at 16:12 | |||||
| Jun 28, 2019 at 15:03 | history | asked | 57Jimmy | CC BY-SA 4.0 |