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On Compact Riemann Surfaces With Dihedral Groups Of Automorphisms


Gamboa Mutuberria, José Manuel and Bujalance, E. and Cirre, F.J. and Gromadzki, G. (2003) On Compact Riemann Surfaces With Dihedral Groups Of Automorphisms. Mathematical Proceedings , 134 (3). pp. 465-477. ISSN 0305-0041

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We study compact Riemann surfaces of genus g 2 having a dihedral group of automorphisms. We find necessary and sufficient conditions on the signature of a Fuchsian group for it to admit a surface kernel epimorphism onto the dihedral group DN.
The question of extendability of the action of DN is considered.
We also give an explicit parametrization of the moduli space of Riemann surfaces with maximal dihedral symmetry, showing that it is a one-dimensional complex manifold.
Defining equations of all such surfaces and the formulae of their automorphisms are calculated.
The locus of this moduli space consisting of those surfaces admitting some real structure is determined.

Item Type:Article
Uncontrolled Keywords:Riemann surfaces; automorphism groups; moduli space
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15255

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