Timeline for Complex curves covered by smooth plane curves
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 7, 2013 at 14:18 | comment | added | Jason Starr | I don't know the answer, and this actually sounds difficult. Obviously, even when $C$ has general moduli among genus $g$ curves, a finite cover $C'$ does not need to have general moduli. This question does vaguely remind me of work of Bogomolov and Tschinkel: every curve over the algebraic closure of a finite field has a finite cover that is also an etale cover of a (fixed) hyperelliptic curve. | |
| Jan 7, 2013 at 8:31 | history | edited | aglearner | CC BY-SA 3.0 |
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| Jan 7, 2013 at 5:32 | comment | added | aglearner | I would be happy with any counter-example but after some thinking it seems to me that the answer to this question might be positive... | |
| Jan 7, 2013 at 4:24 | history | edited | aglearner | CC BY-SA 3.0 |
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| Jan 6, 2013 at 23:05 | answer | added | Michael Zieve | timeline score: 1 | |
| Jan 6, 2013 at 22:25 | comment | added | Felipe Voloch | @Piotr If $C: y^2=f(x)$ is hyperelliptic with $f$ of even degree $2n$, then $y^{2n}=f(x)$ is smooth and covers $C$. I suspect the answer to the general question is no, but I don't know how to do it. Maybe the answer that Jason Starr gave to a recent question of Mike Zieve will work here too. | |
| Jan 6, 2013 at 22:08 | comment | added | Piotr Achinger | Do you know if this is true for $C$ a hyperelliptic curve of genus 2 or 3? | |
| Jan 6, 2013 at 21:17 | history | asked | aglearner | CC BY-SA 3.0 |