Persona: Costa González, Antonio Félix
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Costa González
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Antonio Félix
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Publicación The NSSC (Nec Subgroups Signature Calculation) Package(2017) Cortázar, Ismael; Costa González, Antonio FélixPublicación On the connectedness of the branch locus of moduli space of hyperelliptic Klein surfaces with one boundary(2015-01-01) Izquierdo, Milagros; Costa González, Antonio Félix; Porto Ferreira da Silva, Ana MaríaAbstract. In this work we prove that the hyperelliptic branch locus of ori- entable Klein surfaces of genus g with one boundary component is connected and in the case of non-orientable Klein surfaces it has g+1 2 components, if g is odd, and g+2 2 components for even g. We notice that, for non-orientable Klein surfaces with two boundary components, the hyperelliptic branch loci are connected for all genera.Publicación On Riemann surfaces of genus g with 4g automorphisms(2016-04-01) Izquierdo Barrios, Milagros; Bujalance García, Emilio; Costa González, Antonio FélixWe 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.Publicación Computing the signatures of subgroups of non-Euclidean crystallographic groups(2017) Cortázar, Ismael; Costa González, Antonio FélixA (planar and cocompact) non-Euclidean crystallographic (NEC) group is a subgroup of the group of (conformal and anti-conformal) isometries of the hyperbolic plane H2 such that H2= is compact. NEC groups are classifed alge- braically by a symbol called signature. In this symbol there is a sign + or and, in the case of sign +, some cycles of integers called period-cycles have an essential direction. In 1990 A.H.M. Hoare gives an algorithm to obtain the signature of a nite index subgroup of an NEC group. The process of Hoare fails in some cases in the task of computing the direction of period-cycles. In this work we complete the algorithm of Hoare, this allows us to construct a program for computing the signature of subgroups of NEC groups in all cases.Publicación Note on topologically singular points in themoduli space of Riemann surfaces of genus 2(Springer, 2019-06-20) Costa González, Antonio Félix; Porto Ferreira da Silva, Ana MaríaLet Mg be the moduli space of Riemann surfaces of genus g. Rauch (Bull Am Math Soc 68:390–394, 1962) focused his attention on and determined the so-called topological singular points ofMg: these are the points ofMg whose neighbourhoods are not homeomorphic to a ball. In a previous paper, the authors produced a topological proof for Rauch’s result for genera > 2; however, the methods used there do not apply to the genus 2 case. The only known proof for the remaining and important case, i.e., the case of singular points inM2, is to be found in an article by Igusa (Ann Math 72(3):612–649, 1960) and it lays on methods from algebraic geometry. Here, we present a topological proof for this case too.