Realizing alternating groups as monodromy groups of genus one covers

Abstract

We prove that if n ≥ 4, a generic Riemann surface of genus 1 admits a meromorphic function (i.e., an analytic branched cover of IP) of degree n such that every branch point has multiplicity 3, and the monodromy group is the alternating group An. To prove this theorem, we construct a Hurwitz space and show that it maps (generically) onto the genus one moduli… (More)

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Cite this paper

@inproceedings{Fried2007RealizingAG, title={Realizing alternating groups as monodromy groups of genus one covers}, author={Mike Fried and Eric Klassen and Yaacov Kopeliovich}, year={2007} }