Apuntes para un estudio socio-económico de la espeleología en nuestro país

[spa] Parece que nunca nos hemos detenido a pensar en las consecuencias que arrastra nuestra común afición espeleológica. Parece que la Espeleología del país es pobre en recursos económicos y sus practicantes e investigadores no disponen de medios algunos a su alcance para mejor desarrollar la actividad. Estos apuntes pretenden despejar posibles dudas y exponer unas "páginas blancas" de nuestra Espeleología, que si el Consejo de Redacción de "ENDINS" y los medios económicos lo permiten, aparecerán en números sucesivos de nuestra publicación

Finite morphisms and Nash multiplicity sequences

We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varietie

Time resolved pattern evolution in a large aperture laser

We have measured quasi-instantaneous transverse patterns in a broad aperture laser. Non-ordered patterns yielding to boundary determined regular structures in progressive time-integrated recording are observed. The linear analysis and numerical integration of the full Maxwell-Bloch equations allow us to interpret the features of the experiment. We show that this system being far from threshold cannot be fully understood with a perturbative model.Comment: 7 pages, 5 GIF figures . To be published in Phys. Rev. Let

Nash multiplicity sequences and Hironaka's order function

When X is a d-dimensional variety defined over a field k of characteristic zero, a constructive resolution of singularities can be achieved by successively lowering the maximum multiplicity via blow ups at smooth equimultiple centers. This is done by stratifying the maximum multiplicity locus of X by means of the so called resolution functions. The most important of these functions is what we know as Hironaka’s order function in dimension d. Actually, this function can be defined for varieties when the base field is perfect; however if the characteristic of k is positive, the function is, in general, too coarse and does not provide enough information so as to define a resolution. It is very natural to ask what the meaning of this function is in this case, and to try to find refinements that could lead, ultimately, to a resolution. In this paper we show that Hironaka’s order function in dimension d can be read in terms of the Nash multiplicity sequences introduced by Lejeune-Jalabert. Therefore, the function is intrinsic to the variety and has a geometrical meaning in terms of its space of arcs.The authors were partially supported by MTM2015-68524-P. The third author was supported by BES-2013-062656

On some properties of the asymptotic Samuel function

The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel Slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.Comment: 21 page

Contact loci and Hironaka's order

We study contact loci sets of arcs and the behavior of Hironaka’s order function defined in constructive Resolution of singularities. We show that this function can be read in terms of the irreducible components of the contact loci sets at a singular point of an algebraic variety.The authors were partially supported by MTM2015-68524-P; The first author was partially supported from the Spanish Ministry of Economy and Competitiveness, through the "Severo Ochoa" Programme for Centres of Excellence in R&D (SEV-2015-0554)