A necessary and sufficient condition for lifting the hyperelliptic involution

Turbek, Peter

doi:10.1090/S0002-9939-97-03934-8

A necessary and sufficient condition for lifting the hyperelliptic involution
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Proc. Amer. Math. Soc. 125 (1997), 2615-2625 Request permission

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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