A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ϱ, called a p-hyperelliptic involution, for which X/ϱ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-12,
author = {Ewa Tyszkowska},
title = {On pq-hyperelliptic Riemann surfaces},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {115-120},
zbl = {1080.30037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-12}
}
Ewa Tyszkowska. On pq-hyperelliptic Riemann surfaces. Colloquium Mathematicae, Tome 103 (2005) pp. 115-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-12/