Toric embedded resolutions of quasi-ordinary hypersurface singularities

We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485-503. In the first procedure the singularity is embedded as hypersurface. In the second procedure, which is inspired by a work of Goldin and Teissier for plane curves (see Resolving singularities of plane analytic branches with one toric morphism,loc. cit., pages 315-340), we re-embed the singularity in an affine space of bigger dimension in such a way that one toric morphism provides its embedded resolution. We compare both procedures and we show that they coincide under suitable hypothesis.Comment: To apear in Annales de l'Institut Fourier (Grenoble

Bijectiveness of the Nash Map for Quasi-Ordinary Hypersurface Singularities

In this paper we give a positive answer to a question of Nash concerning the arc space of a singularity, for the class of quasi-ordinary hypersurface singularities, extending to this case previous results and techniques of Shihoko Ishii.Comment: comments and references adde

Toric Geometry and the Semple-Nash modification

This paper proposes some material towards a theory of general toric varieties without the assumption of normality. Their combinatorial description involves a fan to which is attached a set of semigroups subjected to gluing-up conditions. In particular it contains a combinatorial construction of the blowing up of a sheaf of monomial ideals on a toric variety. In the second part it is shown that over an algebraically closed base field of zero characteristic the Semple-Nash modification of a general toric variety is isomorphic to the blowing up of the sheaf of logarithmic jacobian ideals and that in any characteristic this blowing-up is an isomorphism if and only if the toric variety is non singular. In the second part we prove that orders on the lattice of monomials (toric valuations) of maximal rank are uniformized by iterated Sempla-Nash modifications.Comment: New version. Appeared in "Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A Matematicas", October 2012 (Electronic

Multi-Harnack smoothings of real plane branches

We introduce a new method for the construction of smoothings of a real plane branch $(C, 0)$ by using Viro Patchworking method. Since real plane branches are Newton degenerated in general, we cannot apply Viro Patchworking method directly. Instead we apply the Patchworking method for certain Newton non degenerate curve singularities with several branches. These singularities appear as a result of iterating deformations of the strict transforms of the branch at certain infinitely near points of the toric embedded resolution of singularities of $(C,0)$. We characterize the $M$-smoothings obtained by this method by the local data. In particular, we analyze the class of multi-Harnack smoothings, those smoothings arising in a sequence $M$-smoothings of the strict transforms of (C,0) which are in maximal position with respect to the coordinate lines. We prove that there is a unique the topological type of multi-Harnack smoothings, which is determined by the complex equisingularity type of the branch. This result is a local version of a recent Theorem of Mikhalkin

Motivic Milnor fiber of a quasi-ordinary hypersurface

Let $f$ be a germ of complex analytic function at $({\mathbf{C}}^{d+1}, 0)$ such that its zero level defines an irreducible germ of quasi-ordinary hypersurface $(S,0)$. We describe the motivic Igusa zeta function, the motivic Milnor fibre and the Hodge-Steenbrink spectrum of $f$ at 0 in terms of topological invariants of the quasi-ordinary hypersurface $(S,0)$

Decomposition in bunches of the critical locus of a quasi-ordinary map

A polar hypersurface P of a complex analytic hypersurface germ, f=0, can be investigated by analyzing the invariance of certain Newton polyhedra associated to the image of P, with respect to suitable coordinates, by certain morphisms appropriately associated to f. We develop this general principle of Teissier (see Varietes polaires. I. Invariants polaires des singularites d'hypersurfaces, Invent. Math. 40 (1977), 3, 267-292) when f=0 is a quasi-ordinary hypersurface germ and P is the polar hypersurface associated to any quasi-ordinary projection of f=0. We build a decomposition of P in bunches of branches which characterizes the embedded topological type of the irreducible components of f=0. This decomposition is characterized also by some properties of the strict transform of P by the toric embedded resolution of f=0 given by the second author in a paper which will appear in Annal. Inst. Fourier (Grenoble). In the plane curve case this result provides a simple algebraic proof of the main theorem of Le, Michel and Weber in "Sur le comportement des polaires associees aux germes de courbes planes", Compositio Math, 72, (1989), 1, 87-113

Experiencia docente universitaria mediante el uso de metodologías activas para el aprendizaje como la evaluación formativa compartida y el trabajo de competencias transversales

[EN] This work shows an active methodology for university teaching through cooperative learning and learning assessment conducted through the collaborative formative assessment, all mediated by the transversal skills of teamwork and communicative of public speaking. The research methodology consisted of comparing the marks obtained in the same subject prior to implement the cooperative learning and collaborative formative assessment with the ones obtained after their use. The results show that the use of tools of cooperative learning and participatory and formative assessment originate better learning in students in relation to older and more traditional teaching-learning and assessment methods, also increases their involvement and learning, taken advantage of those to further enhance their skills of teamwork and public speaking communication.[ES] Este trabajo muestra una metodología activa para la enseñanza universitaria a través del aprendizaje cooperativo y la evaluación de los aprendizajes realizada a través de la evaluación formativa compartida, todo ello vehiculizado con las competencias transversales de trabajo en equipo y comunicativa de hablar en público.La metodología de investigación ha consistido en comparar las calificaciones obtenidas en la misma asignatura con anterioridad a implementar el aprendizaje cooperativo y la evaluación compartida formativa, con las obtenidas después de utilizarla. Los resultados demuestran que la utilización de herramientas de aprendizaje cooperativo y de evaluación participativa y formativa originan un mejor aprendizaje en el alumnado en relación a metodologías más antiguas y tradicionales de enseñanza-aprendizaje y evaluación, esta nueva metodología aumenta su implicación y aprendizaje, la cual se aprovecha para potenciar asimismo sus competencias de trabajo en equipo y comunicativa de hablar en público.Trigueros Preciados, S.; Perez Gonzalez, D.; Solana González, P.; García Ruiz, E. (2016). Experiencia docente universitaria mediante el uso de metodologías activas para el aprendizaje como la evaluación formativa compartida y el trabajo de competencias transversales. En In-Red 2016. II Congreso nacional de innovación educativa y docencia en red. Editorial Universitat Politècnica de València. https://doi.org/10.4995/INRED2016.2016.4351OC

A case analysis of a product lifecycle information management framework for SMEs.

Information management during the product lifecycle has received a great deal of attention over the last few years, mainly because firms work in a complex business environment characterized by information overload, high levels of competitiveness and the acceleration of technological change. In this context, Product Lifecycle Management(PLM) software has been evolving rapidly and,today, powerfultools in the market enable high levels of information to be managed. However, commercial PLM software is mostly oriented towards large-sized firms, which poses a big challenge for small and mid-sized enterprises (SMEs). To address this issue, SMEs can develop their own Product Lifecycle Information Management (PLIM) Frameworks for managing data and information throughout the product lifecycle processes. This article presents a successful example of a PLIM Framework: the case of Pladomin’s PLIM Framework