Persona:
Costa González, Antonio Félix

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ORCID
0000-0002-9905-0264
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Costa González
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Antonio Félix
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2016 - 201912020 - 20251
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Autor: Bujalance García, Emilio × search.filters.applied.f.itemFacultad: Facultad de Ciencias ×

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Mostrando 1 - 2 de 2
  • Miniatura
    Publicación
    On Riemann surfaces of genus g with 4g automorphisms
    (2016-04-01) Izquierdo Barrios, Milagros; Bujalance García, Emilio; Costa González, Antonio Félix
    We determine, for all genus g 2 the Riemann surfaces of genus g with exactly 4g automorphisms. For g 6= 3; 6; 12; 15 or 30, this sur- faces form a real Riemann surface Fg in the moduli space Mg: the Riemann sphere with three punctures. We obtain the automorphism groups and extended automorphism groups of the surfaces in the fam- ily. Furthermore we determine the topological types of the real forms of real Riemann surfaces in Fg. The set of real Riemann surfaces in Fg consists of three intervals its closure in the Deligne-Mumford com- pacti cation of Mg is a closed Jordan curve. We describe the nodal surfaces that are limits of real Riemann surfaces in Fg.
  • Miniatura
    Publicación
    Fenchel’s conjecture on NEC groups
    (Springer, 2025-08-20) Bujalance García, Emilio; Cirre Torres, Francisco Javier; Conder, Marston D. E.; Costa González, Antonio Félix; Agencia Estatal de Investigación
    A classical discovery known as Fenchel's conjecture and proved in the 1950s, shows that every co-compact Fuchsian group has a normal subgroup of finite index isomorphic to the fundamental group of a compact unbordered orientable surface, or in algebraic terms, that has a normal subgroup of finite index that contains no element of finite order other than the identity. In this paper we initiate and make progress on an extension of Fenchel's conjecture by considering the following question: Does every planar non-Euclidean crystallographic group containing transformations that reverse orientation have a normal subgroup of finite index isomorphic to the fundamental group of a compact unbordered non-orientable surface? We answer this question in the affirmative in the case where the orbit space of is a nonorientable surface, and also in the case where this orbit space is a bordered orientable surface of positive genus. In the case where the genus of the quotient is , we have an affirmative answer in many subcases, but the question is still open for others.