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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Abstract:

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.


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Additional Information

Mike Fried
Affiliation: Department of Mathematics, University of California at Irvine, Irvine, California 92717
Email: mfried@math.uci.edu

Eric Klassen
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: klassen@math.fsu.edu

Yaacov Kopeliovich
Affiliation: Unigraphics Solutions, 100824 Hope St., Cypress, California 90630
Email: YKopeliovich@mail101.webango.com

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05736-1
PII: S 0002-9939(00)05736-1
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