No abstract

We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called \emph{translated} components of the characteristic varieties, and shows that the zero-dimensional components are indeed torsion. The main result is used to derive further obstructions for a group to be the fundamental group of a quasi-projective manifold.Comment: 33 pages, no figures. General rearrangement and proof of Proposition 4.2 is expande

In this work we present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in P 2 having a singular point of type A n , n ≥ 15, only rational singularities and global Milnor number at least 18. Moreover, we have developed a method for an explicit construction of sextic curves with at least eight-possibly infinitely near-double points. This method allows one to express such sextic curves in terms of arrangements of curves with lower degrees and it provides a geometric picture of possible deformations. Because of the large number of cases, we have chosen to carry out only a few to give some insights into the general situation.

The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function Z DL (h, T ) of a quasi-ordinary power series h of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent Z DL (h, T ) = P (T )/Q(T ) such that almost all the candidate poles given by Q(T ) are poles. Anyway, these candidate poles give eigenvalues of the monodromy action of the complex of nearby cycles on h −1 (0). In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if h is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.

ABSTRACT. -In this work we give a formula for the local Denef-Loeser zeta function of a superisolated singularity of hypersurface in terms of the local Denef-Loeser zeta function of the singularities of its tangent cone. We prove the monodromy conjecture for some surfaces singularities. These results are applied to the study of rational arrangements of plane curves whose Euler-Poincaré characteristic is three.