On the monodromy at infinity of a polynomial map
Hodge numbers attached to a polynomial map
We attach a limit mixed Hodge structure to any polynomial map . The equivariant Hodge numbers of this mixed Hodge structure are invariants of which reflect its asymptotic behaviour. We compute them for a generic class of polynomials in terms of equivariant Hodge numbers attached to isolated hypersurface singularities and equivariant Hodge numbers of cyclic coverings of projective space branched along a hypersurface. We show how these invariants allow to determine topological invariants of such...
Topological computation of local cohomology multiplicities.
We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link.
Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility
In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a plane branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two variables and necessary conditions which a complex curve has to satisfy in order to be the discriminant of a complex plane branch.
Pinceaux de courbes planes et invariants polaires
We study pencils of plane curves , t ∈ ℂ, using the notion of polar invariant of the plane curve f = 0 with respect to a smooth curve l = 0. More precisely we compute the jacobian Newton polygon of the generic fiber , t ∈ ℂ. The main result gives the description of pencils which have an irreducible fiber. Furthermore we prove some applications of the local properties of pencils to singularities at infinity of polynomials in two complex variables.
Extension of multilinear operators on Banach spaces.
These notes deal with the extension of multilinear operators on Banach spaces. The organization of the paper is as follows. In the first section we study the extension of the product on a Banach algebra to the bidual and some related structures including modules and derivations. Tha approach is elementary and uses the classical Arens' technique. Actually most of the results of section 1 can be easily derived from section 2. In section 2 we consider the problem of extending multilinear forms on a...
Diseños muestrales π-equivalentes y equivalentes de primer orden.
El comportamiento de un diseño muestral en relación al estimador de Horvitz-Thompson depende exclusivamente de sus probabilidades de inclusión de primer y segundo orden. Al ser, usualmente, mucho mayor el número de muestras de un diseño que el número de dichas probabilidades de inclusión, fijadas éstas, existen una gran cantidad de diseños que las satisfacen y que por ello proporcionan similares resultados en relación al mencionado estimador, siendo posible escoger entre los mismos aquellos que...
Characterization of non-degenerate plane curve singularities.
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