Questions tagged [hurwitz-theory]

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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 ...
Arun Debray's user avatar
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5 votes
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256 views

Connected relative Gromov Witten invariants

I am currently interested to compute relative Gromov Witten invariants(GW) over $\mathbb{P}^1$. In the paper https://arxiv.org/pdf/math/0204305.pdf eq 3.1 gives the count of relative disconnected GW ...
GGT's user avatar
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4 votes
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Generalising definition of Hurwitz number of compactified moduli space of curve

I am asking mostly for reference if such a definition exists in the literature. I am also interested in the count if it appears somewhere. Let $\mu:=(\mu_1,\ldots , \mu_n)\vdash d$ for positive ...
GGT's user avatar
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3 votes
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Which invertible linear maps preserve the set of Hurwitz stable matrices?

Let $V = M_n(\mathbb{R})$ be the set of all $n\times n$ matrices with real elements and $V_{-}$ be a subset of Hurwitz stable matrices, i.e. matrices such that all their eigenvalues have strictly ...
Fiktor's user avatar
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2 votes
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Cut and Join for Hurwitz number with multiple spin

Let me introduce some background of cut and join equation for spin Hurwitz number with the completed cycle as mentioned in https://arxiv.org/pdf/1103.3120.pdf We fix two partition $\mu $ and $\nu$ of ...
GGT's user avatar
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2 votes
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A version of Hurwitz' theorem in terms of Euler characteristic

Page 203 of Farb and Margalit's Primer on Mapping Class Groups contains the result: Let $g ≥ 2$. The order of any finite subgroup of $MCG(S_g)$ is at most $84(g − 1)$. I've been told by my ...
Yossarian's user avatar
1 vote
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Is this an explicit construction of a Hurwitz space with Galois group Z/p, p distinct branch points, and inertia group Z/(p-1)?

I am desperately confused and would like a sanity check that the following moduli space/stack is a Hurwitz space/stack. I would also appreciate any references on the topic of the explicit construction ...
Catherine Ray's user avatar
1 vote
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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 ...
Nati's user avatar
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