Unramified Double Coverings of Hyperelliptic Surfaces. II

Abstract

In this note we illustrate how to count the fixed points of a lift of the hyperelliptic involution to a smooth unramified double cover. In this way we obtain a new proof of the assertion that only $\left ( {\begin {array}{*{20}{c}} {2g + 2} \\ 2 \\ \end {array} } \right )$ of the double covers are hyperelliptic and classify the remaining covers in terms of $\tilde g$-hyperellipticity.