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 | References | Similar Articles | Additional Information

Abstract: Let 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 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