On a theorem of accola

Abstract

In these notes we generalize the following result due to R. Accola: Given a hyperelliptic Riemann surface S of genus g⩽2 and n a non-negative integer, there is a smooth n-sheeted covering , where R is a hyperelliptic Riemann surface. We show that the above result extends to the family of η-hyperelliptic Riemann surfaces as: Given a η-hyperelliptic Riemann surface S of genus g⩽2, a η-hyperelliptic involution τ:S→S and a non-negative integer n, there is a smooth n-sheeted covering , where R is a hyperelliptic Riemann surface for which τ lifts as a -hyperelliptic involution, and