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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.
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
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
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
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
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
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
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
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
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
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
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