Let $X$ be a symmetric compact Riemann surface whose full group of
conformal automorphisms is cyclic. We derive a formula for counting
the number of ovals of the symmetries of $X$ in terms of few data of
the monodromy of the covering $X\rightarrow X/G$, where
$G=\mbox{\rm Aut\/}^\pm X$ is the full group of conformal and
anticonformal automorphisms of $X$.
@article{1218475347,
author = {Bujalance
,
Emilio and Cirre
,
Francisco Javier and Gamboa
,
Jos\'e Manuel and Gromadzki
,
Grzegorz},
title = {On the number of ovals of a symmetry of a compact Riemann surface},
journal = {Rev. Mat. Iberoamericana},
volume = {24},
number = {2},
year = {2008},
pages = { 391-405},
language = {en},
url = {http://dml.mathdoc.fr/item/1218475347}
}
Bujalance
,
Emilio; Cirre
,
Francisco Javier; Gamboa
,
José Manuel; Gromadzki
,
Grzegorz. On the number of ovals of a symmetry of a compact Riemann surface. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp. 391-405. http://gdmltest.u-ga.fr/item/1218475347/