Open Access
Translator Disclaimer
October, 2004 Real Schottky Uniformizations and Jacobians of May Surfaces
Rubén A. Hidalgo, Rubí E. Rodríguez
Rev. Mat. Iberoamericana 20(3): 627-646 (October, 2004).


Given a closed Riemann surface $R$ of genus $p \geq 2$ together with an anticonformal involution $\tau:R \to R$ with fixed points, we consider the group $K(R,\tau)$ consisting of the conformal and anticonformal automorphisms of $R$ which commute with $\tau$. It is a well known fact due to C. L. May that the order of $K(R,\tau)$ is at most $24(p-1)$ and that such an upper bound is attained for infinitely many, but not all, values of $p$. May also proved that for every genus $p \geq 2$ there are surfaces for which the order of $K(R,\tau)$ can be chosen to be $8p$ and $8(p+1)$. These type of surfaces are called \textit{May surfaces}. In this note we construct real Schottky uniformizations of every May surface. In particular, the corresponding group $K(R,\tau)$ lifts to such an uniformization. With the help of these real Schottky uniformizations, we obtain (extended) symplectic representations of the groups $K(R,\tau)$. We study the families of principally polarized abelian varieties admitting the given group of automorphisms and compute the corresponding Riemann matrices, including those for the Jacobians of May surfaces.


Download Citation

Rubén A. Hidalgo. Rubí E. Rodríguez. "Real Schottky Uniformizations and Jacobians of May Surfaces." Rev. Mat. Iberoamericana 20 (3) 627 - 646, October, 2004.


Published: October, 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1070.30018
MathSciNet: MR2124485

Primary: 14H15 , 30F40
Secondary: 14H40 , 32G20

Keywords: abelian varieties , automorphisms , Jacobians , Kleinian groups

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid


Vol.20 • No. 3 • October, 2004
Back to Top