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Results tagged with riemann-surfaces
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user 3384
Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
1
vote
Fuchsian groups and automorphisms of Riemann surfaces
How about $\Gamma = PSL_2(\mathbf{Z})$, where $N(\Gamma)/\Gamma)$ is the trivial group but the automorphism group of $\Gamma \setminus \mathcal{H}^*$ is infinite?
In general the best you can do is th …
- 3,625
6
votes
Accepted
How does a moduli interpretation give an analytic object an algebraic structure?
Even on the level of sets, the idea that any compact Riemann surface gives rise to an algebraic curve over $\mathbf{Q}$ should feel resoundingly false. There are uncountably many compact Riemann surfa …
- 3,625
5
votes
How do you find the genus of a Fuchsian group derived from a quaternion algebra?
You are essentially asking for a fundamental domain for your Fuchsian group $G$. This is an area of specialty for John Voight, who has produced an algorithm for finding such a fundamental domain and t …
- 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