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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A necessary and sufficient condition
for lifting the hyperelliptic involution


Author: Peter Turbek
Journal: Proc. Amer. Math. Soc. 125 (1997), 2615-2625
MSC (1991): Primary 30F35, 20H10
DOI: https://doi.org/10.1090/S0002-9939-97-03934-8
MathSciNet review: 1401755
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Abstract: Let $X$ denote a Riemann surface which possesses a fixed point free group of automorphisms with a hyperelliptic orbit space. A criterion is proved which determines whether the hyperelliptic involution lifts to an automorphism of $X.$ Necessary and sufficient conditions are stated which determine when a lift of the hyperelliptic involution is fixed point free. A complete determination is made of the abelian groups which may arise as automorphism groups of surfaces which possess a fixed point free lift.


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Additional Information

Peter Turbek
Affiliation: Department of Mathematics, Statistics, and Computer Science, Purdue University–Calumet, Hammond, Indiana 46323
Email: turbek@nwi.calumet.purdue.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03934-8
Received by editor(s): March 14, 1996
Dedicated: Dedicated to the memory of Sheela Phansalkar (1966-1990)
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1997 American Mathematical Society