Información del autor
Autor Etayo Gordejuela, J. Javier |
Documentos disponibles escritos por este autor (47)
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In this work we give pairs of generators (x, y) for the alternating groups An, 5 ? n ? 19, such that they determine the minimal genus of a Riemann surface on which An acts as the automorphism group. Using these results we prove that A15 is the u[...]texto impreso
The authors obtain the pairs of generators, necessary to study the non-orientable case, of the alternating groups $A_n$ for 21, 22, 28 and 29, which are also Hurwitz groups, groups with maximal number of automorphisms on Riemann surfaces[...]texto impreso
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Bujalance, E. ; Etayo Gordejuela, J. Javier | Department of Mathematics, Tokyo Institute of Technology | 1987If G is a group of automorphisms of a hyperelliptic Riemann surface of genus g represented as D/$\Gamma$ where D is the hyperbolic plane and $\Gamma$ a Fuchsian group, then $G\cong \Gamma '/\Gamma$ where $\Gamma$ ' is also a Fuchsian group. Furt[...]texto impreso
Bujalance, E. ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. | Universidad Complutense de Madrid | 1986The authors describe in terms of non-Euclidean crystallographic groups all Klein surfaces whose automorphism group is one of the following: Z/p???Z/p , Z/pq , or Z/p 2 , where p and q are distinct odd primes. This includes every nontrivial fi[...]texto impreso
Let C be an algebraic curve of genus 3, defined over the real field R. The automorphism group of C is studied in this paper. In a paper by the same authors [Mich. Math. J. 33, 55-74 (1986; see 20043 below)], the hyperelliptic case was solved, th[...]texto impreso
A compact Klein surface with boundary of algebraic genus g?2 has at most 12(g?1) automorphisms. When a surface attains this bound we say that it has maximal symmetry, and the group of automorphisms is then an M group. In this paper we exhibit fo[...]texto impreso
A compact Klein surface X is called q-hyperelliptic if there is an involution $\phi$ of X such that the quotient surface $X/ $ has algebraic genus q. If X is represented as D/$\Gamma$ where D is the unit disc and $\Gamma$ a non-Euclidean crysta[...]texto impreso
Bujalance, E. ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. | Real Academia de Ciencias Exactas, Físicas y Naturales | 1984The classical correspondence between Riemann surfaces and complex algebraic curves, extends by the work of Ailing and Greenleaf to Klein surfaces and real algebraic curves. The topological invariants of the surface determine the ones of a smonot[...]texto impreso
Elliptic-hyperelliptic, normal, unramified, double coverings of bordered hyperelliptic Klein surfaces are considered here, using methods of the theory on non-Euclidean crystallographic groups. Complete proofs will appear elsewheretexto impreso
Todo grupo finito G actúa como grupo de automorfismos de diversas superficies de Klein con borde. Al menor de los géneros algebraicos de estas superficies se le llama género real ?(G) del grupo G. Se conocen todos los grupos con0 ? ?(G) ? 8, as?[...]texto impreso
Castrillón López, Marco ; Díaz-Cano Ocaña, Antonio ; Etayo Gordejuela, J. Javier ; Folgueira, Marta ; Infante del Río, Juan Antonio ; Pozo Coronado, Luis Miguel ; Rey Cabezas, Jose María | No publicado | 2013Material elaborado por profesores de la UCM para la asignatura de este nombre del grado en Ingeniería Matemáticas, el grado en Matemáticas y el grado en Matemáticas y Estadística. Contenidos: - Números enteros. Dígitos de control y criptografía[...]texto impreso
The authors establish that an elliptic-hyperelliptic Klein surface of genus p > 5 generically has at most 4(p-1)automorphisms, excepting the case X is orientable with 2 or 4 boundary components. If X is orientable with 2 or 4 boundary componen[...]texto impreso
En el polígono hiperbólico con todos los águlos rectos, se obtienen fórmulas explícitas parael coseno y el seno y el seno hiperbólicos de la longitud de un lado l en función de las longintudes de los N-3 lados dictintos a l y a sus adyacentes. T[...]texto impreso
Etayo Gordejuela, J. Javier ; Martínez García, Ernesto | Matematisk Institut, Universitetsparken NY Munkegade | 2004We construct a special type of fundamental regions for any Fuchsian group $F$ generated, by an even number of half-turns, and for certain non-Euclidean crystallographic groups (NEC groups in short). By comparing these regions we give geometrical[...]texto impreso
The order of a group of automorphisms of a compact Klein surface of genus 3 with boundary does not exceed 24 [see C. L. May, Pac. J. Math. 59, 199-210 (1975; Zbl 0422.30037)]. These groups of automorphisms are quotients of NEC groups of isometri[...]texto impreso
Beardon gave a procedure for constructing a polygon with prescribed angles. For each ordered set of angles Beardon's polygon is unique up to congruence. The polygon obtained this way has an inscribed circle. It is possible to obtain by means of [...]texto impreso
A compact Klein surface can be represented in the form D/? where D denotes the hyperbolic plane and ? a non-Euclidean crystallographic (N.E.C.) group of isometries. If ? + denotes the subgroup of orientation-preserving isometries, then D/? [...]texto impreso
A Klein surface S is a surface with a dianalytic structure. If S is compact then its underlying topological surface can be orientable or nonorientable and may have boundary. The genus of S is then defined to be the genus of its canonical doub[...]texto impreso
A bordered Klein surface of algebraic genus p has at most 12(p-1) automorphisms and this is attained for infinitely many values of p. Furthermore, for an infinity of values of p, the largest group of automorphisms of such a surface is $4(p+1)$ o[...]texto impreso
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Bujalance, E. ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. ; Martens, Gerriet | Birkhäuser Verlag | 1989Let K be a compact Klein surface of algebraic genus $g\ge 2,$ which is not a classical Riemann surface. The authors show that if K admits an automorphism of order $N> 2,$ then it must have algebraic genus at least $(p\sb 1-1)N/p\sb 1$ if N is pr[...]texto impreso
The author studies the number of fixed points of the elements of an odd order cyclic group of automorphisms of a nonorientable Klein surface by means of non-Euclidean crystallographic groups.texto impreso
We study cyclic groups of automorphisms of Riemann surfaces that contain non-orientable elements. We obtain conditions for such a group, and calculate the minimum possible genus of the surface on which it acts. As a consequence of these results [...]texto impreso
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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
Bujalance, E. ; Etayo Gordejuela, J. Javier ; Martínez, E. ; Szepietowski, B. | Cambridge Univ Press | 2015This paper is devoted to determine the connectedness of the branch loci of the moduli space of non-orientable unbordered Klein surfaces. We obtain a result similar to Nielsen's in order to determine topological conjugacy of automorphisms of prim[...]texto impreso
The minimum genus problem consists in determining the minimum algebraic genus of a surface on which a viven group G acts. For cyclic groups G this problem on bordered Klein surfaces was solved in 1989. The next step is to fix the number of bound[...]texto impreso
The minimum genus problem consists on determining the minimum algebraic genus of a surface on which a given group G acts. For cyclic groups G this problem on bordered Klein surfaces was solved in 1989. The next step is to fix the number of bound[...]texto impreso
A problem of special interest in the study of automorphism groups of surfaces are the bounds of the orders of the groups as a function of the genus of the surface. May has proved that a Klein surface with boundary of algebraic genus p has at mos[...]texto impreso
Alonso García, María Emilia ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. ; Ruiz Sancho, Jesús María | Real Sociedad Matemática Española;Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas | 1980Dado un espacio T3? (X,T), es posible obtener una compactificación T2 del mismo, mediante ultrafiltros asociados a ciertas bases distinguidas de cerrados de (X,T) (Frink [4]). Se plantea así el problema siguiente: ¿Puede obtenerse toda compactif[...]texto impreso
El objetivo de esta memoria es el estudio de los grupos de automorfismos de las superficies de Klein, el concepto de superficie de Klein surge como extensión del de superficie de Riemann que resulta ser un caso particular. La técnica que hemos u[...]texto impreso
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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
Índice abreviado: 1. Generalidades. Teorema de Lagrange 2. Subgrupos normales. Homomorfismos. Teorema de estructura de los grupos abelianos finitos 3. Grupo de automorfismos. Acción de un grupo sobre un conjunto 4. El teorema de Sylow 5. Grupos [...]texto impreso
Every finite group G may act as an automorphism group of Klein surfaces either bordered or unbordered either orientable or non-orientable. For each group the minimum genus receives different names according to the topological features of the sur[...]texto impreso
An important problem in the study of Riemann and Klein surfaces is determining their full automorphism groups. Up to now only very partial results are known, concerning surfaces of low genus or families of surfaces with special properties. This [...]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 [...]texto impreso
Every finite group G acts as an automorphism group of several bordered compact Klein surfaces. The minimal genus of these surfaces is called the real genus and denoted by ?(G). The systematical study was begun by C.L. May and continued by him in[...]texto impreso
A Klein surface with boundary of algebraic genus $\mathfrak{p}\geq 2$, has at most $12(\mathfrak{p}-1)$ automorphisms. The groups attaining this upper bound are called $M^{\ast}$-groups, and the corresponding surfaces are said to have maximal sy[...]texto impreso
Every finite group acts as an automorphism group of several bordered compact Klein surfaces. The minimal genus of these surfaces is called the real genus of and it is denoted The systematical study of this parameter was begun by May and continue[...]texto impreso
Etayo Gordejuela, J. Javier ; Gromadzki, G. ; Martínez García, Ernesto | University of Houston | 2012Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric crosscap number and denoted by ?˜(G). The systematic study about the symmetric[...]texto impreso
Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric cross-cap number and denoted by ˜?(G). This number is related to other paramet[...]texto impreso
Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric crosscap number and denoted by (sigma) over tilde (G). It is known that 3 cann[...]texto impreso
Given a natural number p, a projective irreducible smooth algebraic curve V defined over R is called p-hyperelliptic if there exists a birational isomorphism of V, of order 2, such that V/ has genus p. This work is concerned with the existence o[...]