Revista Matemática Iberoamericana


Full-Text PDF (178 KB) | Metadata | Table of Contents | RMI summary
Volume 24, Issue 2, 2008, pp. 391–405
DOI: 10.4171/RMI/540

Published online: 2008-08-31

On the number of ovals of a symmetry of a compact Riemann surface

Emilio Bujalance[1], Francisco Javier Cirre[2], José Manuel Gamboa[3] and Grzegorz Gromadzki[4]

(1) UNED, Madrid, Spain
(2) UNED, Madrid, Spain
(3) Universidad Complutense de Madrid, Spain
(4) University of Gdańsk, Poland

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 $X$.

Keywords: Riemann surface, symmetries, ovals

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 24 (2008), 391-405. doi: 10.4171/RMI/540