Automorphism groups of cyclic p-gonal pseudo-real Riemann surfaces

Bujalance, E.; Costa, Antonio F.

doi:10.1016/j.jalgebra.2015.06.020

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…In [8,14,18] there is some study of (γ, n)-gonal pairs and their groups of automorphisms when n is prime integer and the n-gonal map is a regular branched cover.…”

Section: Introductionmentioning

confidence: 99%

Uniformizations of stable $(γ,n)$-gonal Riemann surfaces

Hidalgo

2017

Preprint

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A (γ, n)-gonal pair is a pair (S , f ), where S is a closed Riemann surface and f : S → R is a degree n holomorphic map onto a closed Riemann surface R of genus γ. If the signature of (S , f ) is of hyperbolic type, then there is pair (Γ, G), called an uniformization of (S , f ), where G is a Fuchsian group acting on the unit disc D containing Γ as an index n subgroup, so that f is induced by the inclusion of Γ < G. The uniformization is uniquely determined by (S , f ), up to conjugation by holomorphic automorphisms of D, and it permits to provide natural complex orbifold structures on the Hurwitz spaces parametrizing (twisted) isomorphic classes of pairs topologically equivalent to (S , f ). In order to produce certain compactifications of these Hurwitz spaces, one needs to consider the so called stable (γ, n)-gonal pairs, which are natural geometrical deformations of (γ, n)gonal pairs. Due to the above, it seems interesting to search for uniformizations of stable (γ, n)-gonal pairs, in terms of certain class of Kleinian groups. In this paper we review such uniformizations by using noded Fuchsian groups, which are (geometric) limits of quasiconformal deformations of Fuchsian groups, and which provide uniformizations of stable Riemann orbifolds. These uniformizations permit to obtain a compactification of the Hurwitz spaces with a complex orbifold structure, these being quotients of the augmented Teichmüller space of G by a suitable finite index subgroup of its modular group.

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“…In [8,14,18] there is some study of (γ, n)-gonal pairs and their groups of automorphisms when n is prime integer and the n-gonal map is a regular branched cover.…”

Section: Introductionmentioning

confidence: 99%

Uniformizations of stable $(γ,n)$-gonal Riemann surfaces

Hidalgo

2017

Preprint

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Abelian Actions on Pseudo-real Riemann Surfaces

2023

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A compact Riemann surface is called pseudo-real if it admits orientation-reversing automorphisms but none of them has order two. In this paper, we find necessary and sufficient conditions for the existence of an action on a pseudo-real surface of genus $$g\geqslant 2$$ g ⩾ 2 of an abelian group containing orientation-reversing automorphisms. Several consequences are obtained, such as the solution of the minimum genus problem for such abelian actions.

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Uniformizations of stable $$(\gamma ,n)$$ ( γ , n ) -gonal Riemann surfaces

Hidalgo

2018

Anal.Math.Phys.

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Automorphism groups of cyclic p-gonal pseudo-real Riemann surfaces

Cited by 5 publications

References 20 publications

Uniformizations of stable $(γ,n)$-gonal Riemann surfaces

Uniformizations of stable $(γ,n)$-gonal Riemann surfaces

Abelian Actions on Pseudo-real Riemann Surfaces

Uniformizations of stable $$(\gamma ,n)$$ ( γ , n ) -gonal Riemann surfaces

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