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Autor Gamboa, J. M. |
Documentos disponibles escritos por este autor (79)
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In this paper we get an effective algorithm to compute all odd orders and ramification indices of homeomorphisms![]()
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In this paper we obtain an effective algorithm to compute all even orders and ramification indices of homeomorphisms of finite order acting on compact surfaces, orientable or not. This completes the case of odd orders, previously studied by the [...]![]()
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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[...]![]()
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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[...]![]()
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For each integer g ? 2 we give the complete list of groups acting as a group of dianalytic automorphisms of a real projective plane with g holes, which, in algebraic terms, correspond to birational automorphisms of real algebraic (M ? 1)-curves.[...]![]()
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Let K be a formally real field with space of orderings X(K). Then Aut(K) operates on X(K). K is said to have the ”dense orbits property” if for any x 2 X(K) the orbit of x is dense in X(K). Fields with the dense orbits property were introduced b[...]![]()
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This paper gives a very good systematic presentation of the equivalence between the algebraic function fields in one variable over the field $\bbfR$ of real numbers and the Klein surfaces. In section 1 Klein surfaces and morphisms between them a[...]![]()
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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[...]![]()
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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 elsewhere![]()
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We consider double and (possibly) branched coverings : X ! X0 between real algebraic curves where X is hyperelliptic. We are interested in the topology of such coverings and also in describing them in terms of algebraic equations. In this artic[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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/? [...]![]()
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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[...]![]()
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We consider normal (possibly) branched, finite-sheeted coverings $ \pi:X\rightarrow X'$ between hyperelliptic real algebraic curves. We are interested in the topology of such coverings and also in describing them in terms of algebraic equations.[...]![]()
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We characterise algebraically closed fields as those for which the first cohomology group tf^fc^On) of the sheaf On of regular functions over kn vanishes for all positive intergers n.![]()
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The author studies the size of the set of hyperplanes which meet a non- zero-dimensional algebraic set V over a real-closed ground field R. More precisely, let us denote by $V\sb c$ the locus of central points of V, i.e., the closure, in the ord[...]![]()
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We prove that any regularly closed semialgebraic set of R", where R is any real closed field and regularly closed means that it is the closure of its interior, is the projection under a finite map of an irreducible algebraic variety in some Rn +[...]![]()
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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[...]![]()
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Fernando Galván, José Francisco ; Gamboa, J. M. ; Ueno, Carlos | Oxford University Press (OUP) | 2011We show that convex polyhedra in R(n) and their interiors are images of regular maps R(n) -> R(n). As a main ingredient in the proof, given an n-dimensional, bounded, convex polyhedron K subset of R(n) and a point p is an element of R(n) \ K, w[...]![]()
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In this article we present versions of Lojasiewicz's inequality and the Nullstellensatz for the ring of bounded semialgebraic functions on an arbitrary semialgebraic set M. We also prove that the classical Lojasiewicz inequality and Nullstellens[...]![]()
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In this work we study how open and closed semialgebraic maps between two semialgebraic sets extend, via the corresponding spectral maps,to the Zariski and maximal spectra of their respective rings of semialgebraic and bounded semialgebraic functions.![]()
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We study open polynomial maps from Iw” to Iw “. For n = p we give a complete characterization, and for p = 2, n 2 3 we obtain some partial information.![]()
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Gamboa, J. M. ; Alonso García, María Emilia ; Ruiz Sancho, Jesús María | Elsevier Science B.V. (North-Holland) | 1985It is well-known that if C is an algebraic curve over the real closed field R and is a total ordering of the function field R(C) of C then there is a semi-algebraic embedding w : (0, 1) ! C such that f 2 R(C) is positive with respect to if and[...]![]()
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It is proved that if p is a prime ideal in the ring S{M) of semialgebraic functions on a semialgebraic set M, the quotient field of S(M)/p is real closed. We also prove that in the case where M is locally closed, the rings S(M) and P(M)—polynomi[...]![]()
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In this paper we generalize an earlier result of the authors, showing that any closed semialgebraic set whose Zariski-closure is irreducible, is the projection under a finite map of an irreducible real algebraic set (see Theorem 3.2 below).![]()
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The authors study some properties of the ring of abstract semialgebraic functions over a constructible subset of the real spectrum of an excellent ring. To be more precise, let X be a constructible subset of the real spectrum of a ring A. The r[...]![]()
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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[...]![]()
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In this work we define a semialgebraic set S Rn to be irreducible if the noetherian ring of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we u[...]![]()
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Let R be a real closed field, S(M) the ring of continuous semialgebraic functions on a semialgebraic set M subset of R-m and S* (M) its subring of continuous semialgebraic functions that are bounded with respect to R. In this work we introduce s[...]![]()
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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[...]![]()
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The paper under review surveys most known results about the following problem: let $X$ be a compact topological surface of algebraic genus $p> 1$, with or without boundary, orientable or not. How to calculate all groups acting as the full automo[...]![]()
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In this work we analyze some topological properties of the remainder partial derivative M := beta(s)*M\M of the semialgebraic Stone-Cech compactification beta(s)*M of a semialgebraic set M subset of R-m in order to 'distinguish' its points from [...]![]()
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In the same vein as the classical Stone–?Cech compactification, we prove in this work that the maximal spectra of the rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set M ? Rn, which are homeomorphic topological sp[...]![]()
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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[...]![]()
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In this article we study the most significant algebraic, topological and functorial properties of the Zariski and maximal spectra of rings of semialgebraic and bounded semialgebraic functions on a semialgebraic set.![]()
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For a formally real field K let X(K) be the space of orderings. The automorphism group Aut(K) of K operates on X(K). K is said to have the ’dense orbits property’ (DOP) if for all 2 X(K) the orbit of is dense in X(K). The study of such fields,[...]![]()
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After describing explicitly all total orderings in the ring R[[x, y]], we prove that each ordering in the quotient field of the ring of germs of real analytic functions at an irreducible point O of a real analytic surface X is defined by a half-[...]![]()
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After describing explicitly all total orderings in the ring R[[x,y]], we prove that each ordering in the quotient field of the ring of germs of real analytic functions at an irreducible point O of a real analytic surface X is defined by a half-b[...]![]()
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We compute the period matrices of the Riemann surfaces given by the equations w2 = z2g+2![]()
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We obtain new necessary conditions for an n-dimensional semialgebraic subset of R-n to be a polynomial image of R-n. Moreover, we prove that a large family of planar bidimensional semialgebraic sets with piecewise linear boundary are images of p[...]![]()
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Let R be a real closed field and n greater than or equal to 2. We prove that: (1) for every finite subset F of R", the semialgebraic set R"\F is a polynomial image of R"; and (2) for any independent linear forms 1, of R", the semialgebraic set {[...]![]()
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A one page proof (using the real spectrum) of the following result: Let f, g : X ! R be a continuous functions on a topological space X, such that f is strictly positive on g?1(0). Then there exist continuous functions u, v and w such that (1 + [...]![]()
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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[...]![]()
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We present several obstructions for a subset S of Rm to be the image of an euclidean space Rn via a polynomial or a regular map f: Rn--> Rm, in terms of the "geometry" of its exterior boundary dS:=ClRm(S)\S![]()
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The author shows there is a non-Archimedean ordering of the field R(x, y), where x and y are algebraically independent over K, for which the identity is the only order-preserving automorphism. The author proves the partly known result that the f[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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 [...]![]()
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In this paper we study the algebraic structure of the hyperelliptic mapping class group of Klein surfaces, which is closely related to the mapping class group of punctured discs. This group plays an important role in the study of the moduli spa[...]![]()
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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[...]