Realizing alternating groups as monodromy groups of genus one covers
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- by Mike Fried, Eric Klassen and Yaacov Kopeliovich PDF
- Proc. Amer. Math. Soc. 129 (2001), 111-119 Request permission
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.References
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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
- Received by editor(s): March 8, 1999
- Published electronically: August 30, 2000
- Communicated by: Michael Stillman
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 111-119
- MSC (1991): Primary 30F10
- DOI: https://doi.org/10.1090/S0002-9939-00-05736-1
- MathSciNet review: 1784019