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Gamboa, J. M. ; Bujalance, E. ; Conder, M.D.E ; Gromadzki, G. ; Izquierdo, Milagros | Elsevier Science | 2002Let X be a Riemann surface. Two coverings p1 : X ? Y1 and p2 : X ? Y2 are said to be equivalent if p2 =’p1 for some conformal homeomorphism ’: Y1 ? Y2. In this paper we determine, for each integer g¿2, the maximum number R(g) of inequivalent ram[...]texto impreso
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. T[...]texto impreso
Etayo Gordejuela, J. Javier ; Gromadzki, G. ; Martínez García, Ernesto | BIRKHAUSER VERLAG AG | 2012In virtue of the Belyi Theorem an algebraic curve can be defined over the algebraic numbers if and only if the corresponding Riemann surface can be uniformized by a subgroup of a Fuchsian triangle group. Such surfaces are known as Belyi surfaces[...]texto impreso
A Riemann surface X is said to be of type (n,m) if its full automorphism group AutX is cyclic of order n and the quotient surface X/AutX has genus m. In this paper we determine necessary and sufficient conditions on the integers n,m,g and ?, whe[...]texto impreso
Gamboa, J. M. ; Bujalance, E. ; Cirre, Francisco ; Gromadzki, G. | Universidad Autónoma Madrid | 2008The set of stationary points of the anticonformal involution (reflection) of a Riemann surface is called an oval. In this paper the total number of ovals of all reflections on a surface is counted provided the group of conformal automorphisms of[...]texto impreso
The nature of the set of points fixed by automorphisms of Riemann or unbordered nonorientable Klein surfaces as well as quantitative formulae for them were found by Macbeath, Izquierdo, Singerman and Gromadzki in a series of papers. The possible[...]texto impreso
Díaz Sánchez, Raquel ; Garijo, Ignacio ; Hidalgo, Rubén A. ; Gromadzki, G. | Elsevier Science | 2010The geometrically finite complete hyperbolic Riemannian metrics in the interior of a handlebody of genus g, having injectivity radius bounded away from zero, are exactly those produced by Schottky groups of rank g; these are called Schottky stru[...]texto impreso
Every finite group acts as a group of automorphisms of some compact bordered Klein surface of algebraic genus g?2 . The same group G may act on different genera and so it is natural to look for the minimum genus on which G acts. This is the mi[...]texto impreso
Gamboa, J. M. ; Broughton, SA ; Bujalance, E. ; Costa, F.A. ; Gromadzki, G. | American Mathematical Society | 1999For all g 2 there is a Riemann surface of genus g whose automorphism group has order 8g+8, establishing a lower bound for the possible orders of automorphism groups of Riemann surfaces. Accola and Maclachlan established the existence of such sur[...]texto impreso
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Gamboa, J. M. ; Broughton, SA ; Bujalance, E. ; Costa, F.A. ; Gromadzki, G. | Elsevier Science | 1996Let X be a compact Riemann surface and Aut(X) be its automorphism group. An automorphism of order 2 reversing the orientation is called a symmetry. The authors together with D. Singerman have been working on symmetries of Riemann surfaces in the[...]texto impreso
Let $X$ be a compact hyperelliptic Riemann surface which admits anti-analytic involutions (also called symmetries or real structures). For instance, a complex projective plane curve of genus two, defined by an equation with real coefficients, gi[...]texto impreso
Bujalance, E. ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. ; Gromadzki, G. | Elsevier Science | 2011A compact Riemann surface X of genus g ? 2 which can be realized as a q-fold, normal covering of a compact Riemann surface of genus p is said to be (q, p)-gonal. In particular the notion of (2, p)-gonality coincides with p-hyperellipticity and [...]
