El espacio de órdenes de funciones algebraicas de una variable

Tesis Univ. Compl. Dpto. de Geometría y Topología. Dir por Tomás Recio Muñíz, leída en Madrid, el 27 de septiembre de 1982.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEProQuestpu

A Positivstellensatz For Rings Of Continuous-Functions

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 + v2)f = 1 + w2 + gu.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

El espacio de órdenes de un cuerpo de funciones algebraicas de una variable

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Geometría y Topología, leída en 1982.ProQuestDepto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set

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 those of M. To that end we prove that the set of points of beta(s)*M that admit a metrizable neighborhood in beta(s)*M equals M-1c boolean OR (Cl beta(s)*M((M) over bar <= 1)\(M) over bar <= 1) where M-1c is the largest locally compact dense subset of M and (M) over bar <= 1 is the closure in M of the set of 1-dimensional points of M. In addition, we analyze the properties of the sets (partial derivative) over capM and (partial derivative) over tildeM of free maximal ideals associated with formal and semialgebraic paths. We prove that both are dense subsets of the remainder partial derivative M and that the differences partial derivative M\(partial derivative) over capM and (partial derivative) over capM\(partial derivative) over tildeM are also dense subsets of partial derivative M. It holds moreover that all the points of (partial derivative) over capM have countable systems of neighborhoods in beta(s)*M.Ministerio de Ciencia e Innovación (MICINN)Universidad Complutense de MadridGAAR GruposDepto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Normal coverings of hyperelliptic real algebraic curves

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. In this article we completely solve these two problems in case $X$ has the maximum number of ovals within its genus. We first analyze the topological features and ramification data of such coverings. For each isomorphism class we then describe a representative, with defining polynomial equations for $X$ and for $X'$, formulae for generators of the covering transformation group, and a rational formula for the covering $\pi:X\rightarrow X'$.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Unbounded convex polyhedra as polynomial images of Euclidean spaces

Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Symmetry types of hyperelliptic Riemann surfaces

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, gives rise to such a surface, and complex conjugation is such a symmetry. In this memoir, the real structures $\tau$ of $X$ are classified up to isomorphism (i.e., up to conjugation). This is done as follows: the number of connected components of the set of fixed points of $\tau$ together with the connectedness or disconnectedness of the complementary set in $X$ classifies $\tau$ topologically; they determine the species of $\tau$, which only depends on the conjugacy class of $\tau$ (however, different conjugacy classes may have identical species). On these grounds, for a given genus $g\ge2$, the authors first give a list of all full groups of analytic and anti-analytic automorphisms of genus $g$ compact hyperelliptic Riemann surfaces. For every such group $G$, the authors compute polynomial equations for a surface $X$ having $G$ as full group and then find the number of conjugacy classes containing symmetries; they also compute a representative $\tau$ in every such class. Finally, they compute the species corresponding to such classes. This memoir is an exhaustive piece of work, going through a case-by-case analysis. The problem for general compact Riemann surfaces dates back to 1893, when {\it F. Klein} [Math. Ann. 42, 1--29 (1893)] first studied it. For zero genus, it is easy. For genus one, that is, for elliptic surfaces, it was solved by {\it N. Alling} ["Real elliptic curves" (1981)]. Partial results for hyperelliptic surfaces of genus two were obtained by {\it E. Bujalance} and {\it D. Singerman} [Proc. Lond. Math. Soc. 51, 501--519 (1985)].Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu