On $pq$-hyperelliptic Riemann surfaces

Ewa Tyszkowska¹

¹ Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland

Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 115-120

Résumé

A compact Riemann surface $X$ of genus $g>1$ is said to be $p$-hyperelliptic if $X$ admits a conformal involution $\varrho$, called a $p$-hyperelliptic involution, for which $X/\varrho$ is an orbifold of genus $p$. If in addition $X$ admits a $q$-hypereliptic involution then we say that $X$ is $pq$-hyperelliptic. We give a necessary and sufficient condition on $p,q$ and $g$ for existence of a $pq$-hyperelliptic Riemann surface of genus $g$. Moreover we give some conditions under which $p$- and $q$-hyperelliptic involutions of a $pq$-hyperelliptic Riemann surface commute or are unique.

Détail

DOI : 10.4064/cm103-1-12

Mots-clés : compact riemann surface genus said p hyperelliptic admits conformal involution varrho called p hyperelliptic involution which varrho orbifold genus addition admits q hypereliptic involution say pq hyperelliptic necessary sufficient condition existence pq hyperelliptic riemann surface genus nbsp moreover conditions under which p q hyperelliptic involutions pq hyperelliptic riemann surface commute unique