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 ( 2 g + 2 2 ) \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 g ~ \tilde g -hyperellipticity.