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Results tagged with algebraic-curves
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user 3384
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
8
votes
Is the number of twists of a curve with a section in a given field finite
Fact 1 (The Hurwitz Bound): If $X$ is a smooth projective connected curve of genus $g\ge 2$ over $\mathbf{C}$ then
$$| Aut_{\mathbf C }(X)| \le 84(g-1)$$
Fact 2: $Aut_\mathbf{C}(X) = Aut_{\overline …
- 3,625
9
votes
Accepted
"Bad" reduction of Shimura curves via dual graphs
inkspot is indeed correct that the component graphs are indeed not generally trees.
As you seem to have deduced for yourself, Cerednik–Drinfeld uniformization is a highly nontrivial concept, and it re …
- 3,625
2
votes
Etale covers of a hyperelliptic curve
Certainly not. Ogg proved in "Real points on Shimura curves" that there are only finitely many Shimura curves (of the form $X^D_0(N)$) which are hyperelliptic. If there is a prime divisor $q$ of $D$ s …
- 3,625
1
vote
Curves which are not covers of P^1 with four branch points
Without pretending to understand Ben Wieland's argument, let me take the Shimura curve suggestion and run with it. In particular, modulo a few details I think the following should be true:
The Shimur …
- 3,625