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Realizing alternating groups as monodromy groups of genus one covers

Authors: Mike Fried, Eric Klassen and Yaacov Kopeliovich
Journal: Proc. Amer. Math. Soc. 129 (2001), 111-119
MSC (1991): Primary 30F10
Published electronically: August 30, 2000
MathSciNet review: 1784019
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We prove that if $n\geq 4$, a generic Riemann surface of genus 1 admits a meromorphic function (i.e., an analytic branched cover of $\mathbb{P}^{1}$) of degree $n$ such that every branch point has multiplicity $3$ and the monodromy group is the alternating group $A_{n}$. To prove this theorem, we construct a Hurwitz space and show that it maps (generically) onto the genus one moduli space.

References [Enhancements On Off] (What's this?)

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Additional Information

Mike Fried
Affiliation: Department of Mathematics, University of California at Irvine, Irvine, California 92717

Eric Klassen
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306

Yaacov Kopeliovich
Affiliation: Unigraphics Solutions, 100824 Hope St., Cypress, California 90630

Keywords: Riemann surface, monodromy group, Hurwitz space
Received by editor(s): March 8, 1999
Published electronically: August 30, 2000
Communicated by: Michael Stillman
Article copyright: © Copyright 2000 American Mathematical Society

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