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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 13 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1242220724

Digital Object Identifier
doi:10.2969/jmsj/06120607

Zentralblatt MATH identifier
05573652

Mathematical Reviews number (MathSciNet)
MR2532903

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

Keywords
Klein surfaces NEC groups automorphism groups fundamental polygons

Citation

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. http://projecteuclid.org/euclid.jmsj/1242220724.


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