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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.


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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
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