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Results tagged with riemann-surfaces
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user 1310
Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
21
votes
Accepted
Teichmuller modular forms and number theory
@David Hansen: Teichmuller modular forms are basically the natural analogue of Siegel modular forms when one considers sections of line bundles on $M_g$ instead of $A_g$. Search for papers by Ichikawa …
- 40.2k
12
votes
Accepted
Unramified map of Riemann surfaces
Let $C \to D$ be a nontrivial finite étale cover and $p \in C$ a point. Then $C \setminus \{p\} \to D$ is still surjective and unramified, but it's not a covering.
- 40.2k
9
votes
Accepted
Cohomology of the genus 2 mapping class group
The possible automorphism groups of a curve of genus two are known very classically, this is usually attributed to Bolza. In his list we find only three prime factors in the orders of the groups: 2,3 …
- 40.2k
6
votes
Automorphisms of genus 6 surfaces
See "The locus of curves with prescribed automorphism group" by Magaard-Shaska-Shpectorov-Völklein, and the references therein.
- 40.2k
6
votes
Accepted
Index of the mapping class group $\Gamma_{g,n}$ inside $\text{Out}(\Pi_{g,n})$
This is surely not the most direct answer. But $\mathrm{Out}(\Pi_{g,1}) \cong \mathrm{Out}(F_{2g})$ surjects onto $\mathrm{GL}(2g,\mathbf Z)$, and the image of $\Gamma_{g,1}$ lands in $\mathrm{Sp}(2g, …
- 40.2k
6
votes
What are the possible automorphism groups of Riemann surfaces of low genus?
To answer your specific question, there is a unique curve of genus three with a 32-element automorphism group, the hyperelliptic curve
$$ y^2 = x^8 - 1.$$
As for any hyperelliptic curve, the automorph …
- 40.2k
5
votes
Accepted
Are Weierstrass points algebraic
Edit: as pointed out by Felipe below, what used to be here was sort of wrong-headed, but I can't delete this answer since it has already been accepted. Anyway you should do what he says: the divisor o …
- 40.2k
4
votes
Reference on Deligne-Mumford compactness for Riemann surfaces
I'm assuming you are not primarily looking for references to papers in algebraic geometry. Maybe http://arxiv.org/abs/1301.0062 is what you are looking for. They construct rigorously the DM-compactifi …
- 40.2k
3
votes
Explicit constant terms of volumes of moduli spaces
The coefficients of these polynomials are top intersection numbers of psi-classes and the class $\kappa_1$ on $\overline M_{g,n}$. That's how Mirzakhani obtained a new proof of the Witten conjecture, …
- 40.2k
3
votes
Does there exist a non-hyperelliptic Riemann surface with automorphism group $C_2\times A_4$?
One thing that should be made more precise is whether you are asking that the automorphism group equals $C_2 \times A_4$ or if it is enough that it contains $C_2 \times A_4$. I'm assuming you mean the …
- 40.2k
3
votes
Reference for homeomorphism between "analytic" compactification of $M_{g,n}$ and Deligne-Mum...
See John Hubbard and Sarah Koch: "An analytic construction of the Deligne-Mumford compactification of the moduli space of curves".
- 40.2k