On generalized groups.
On Klein Surfaces and Dihedral Groups.
On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms
The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p n are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain...
On p-hyperellipticity of doubly symmetric Riemann surfaces.
Studying commuting symmetries of p-hyperelliptic Riemann surfaces, Bujalance and Costa found in [3] upper bounds for the degree of hyperellipticity of the product of commuting (M - q)- and (M - q')-symmetries, depending on their separabilities. Here, we find necessary and sufficient conditions for an integer p to be the degree of hyperellipticity of the product of two such symmetries, taking into account their separabilities. We also give some results concerning the existence and uniqueness of symmetries...
On soluble groups of automorphisms of nonorientable Klein surfaces
We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.
Parametrization of the moduli space of hyperelliptic and symmetric Riemann surfaces.
-hyperelliptic compact nonorientable Klein surfaces without boundary.
Riemann and Klein surfaces with nodes viewed as quotients.
If G is a group of automorphisms that acts properly discontinuously on a Riemann or Klein surface X, then there exists a unique structure of Riemann or Klein surface on X/G such that the projection π: X → X/G is a morphism. The analogous result is not true when we deal with surfaces with nodes. In this paper we give a new definition of a group that acts properly discontinuously on a surface with nodes in order to obtain a similar theorem.
The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces
The full automorphism group of the Kulkarni surface.
The full automorphism group of the Kulkarni surface is explicitly determined. It is employed to give three defining equations of the Kulkarni surface; each equation exhibits a symmetry of the surface as complex conjugation.
The real genus of the alternating groups.
Vector fields on nonorientable surfaces.