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Questions tagged [hurwitz-theory]

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3
votes
0answers
48 views

fundamental domains in H^2 containing large balls

I would like to construct a genus $g$ surface regularly tiled by triangles (for example by 238 triangles). Edmunds-Ewing-Kulkarni prove that the only obstruction to doing this is Euler characteristic ...
8
votes
0answers
101 views

Are spin Hurwitz numbers $r$-spin Hurwitz numbers?

(I think the answer is no, but I'm not sure.) In Hurwitz theory, one counts $n$-fold branched covers $\Sigma'\to\Sigma$ of a Riemann surface $\Sigma$ with fixed ramification data around each branch ...
1
vote
0answers
129 views

Cycles in the Chow ring of the moduli of curves coming from Hurwitz theory

Are there interesting cycles (other then the famous ones such as: Harris and Mumford's gonality divisor, the Gieseker-Petri divisor [which can be realized as the branch locus of a forgetful map from ...
2
votes
1answer
245 views

holomorphic automorphisms of universal cover of configuration spaces

Hello everyone, I have been trying (without success) to determine the following. Let $P$ denote the space of monic polynomials of degree $n$ with complex coefficients, which have distinct roots. It ...
4
votes
3answers
315 views

Automorphism of finite groups and Hurwitz spaces

If $G$ is a finite group, embedded as a transitive subgroup of $S_n$ for some $n$, will every automorphism of $G$ extend to an inner automorphism of $S_n$? I'm trying to connect the language that's ...
5
votes
1answer
287 views

Spaces parametrizing ramified covers of surfaces

Let $\Sigma$ be a surface (let's say oriented and of finite type). We can consider the configuration space $F(\Sigma,n)$ of $n$ ordered distinct points on $\Sigma$, i.e. $\Sigma^n\setminus \Delta$ ...