Journal of the Mathematical Society of Japan

Automorphism groups of $q$-trigonal planar Klein surfaces and maximal surfaces

Beatriz ESTRADA and Ernesto MARTÍNEZ

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A compact Klein surface $X=\mathcal{D}/\Gamma $, where $\mathcal{D}$ denotes the hyperbolic plane and $\Gamma $ is a surface NEC group, is said to be $q$-trigonal if it admits an automorphism $\varphi $ of order $3$ such that the quotient $X/<\varphi >$ has algebraic genus $q$. In this paper we obtain for each $q$ the automorphism groups of $q$-trigonal planar Klein surfaces, that is surfaces of topological genus $0$ with $k\geq 3$ boundary components. We also study the surfaces in this family, which have an automorphism group of maximal order (maximal surfaces). It will be done from an algebraic and geometrical point of view.

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J. Math. Soc. Japan Volume 61, Number 2 (2009), 607-623.

First available in Project Euclid: 13 May 2009

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Zentralblatt MATH identifier

Primary: 30F50: Klein surfaces 14J50: Automorphisms of surfaces and higher-dimensional varieties 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]

Klein surfaces NEC groups automorphism groups fundamental polygons


ESTRADA, Beatriz; MARTÍNEZ, Ernesto. Automorphism groups of q -trigonal planar Klein surfaces and maximal surfaces. J. Math. Soc. Japan 61 (2009), no. 2, 607--623. doi:10.2969/jmsj/06120607.

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