We introduce orbifold Euler numbers for normal surfaces with boundary-divisors. These
numbers behave multiplicatively under finite maps and in the log canonical case we prove …

We study the interplay between the cohomology of the Koszul complex of the partial
derivatives of a homogeneous polynomial f and the pole order filtration P on the cohomology …

We prove a structure theorem for differential operators in the 0-th term of the V-filtration
relative to a free divisor. manifold. As an application, we give a formula for the logarithmic de …

We find explicit free resolutions for the D-modules Df s and D [s] fs/D [s] f s+ 1, where f is a
reduced equation of a locally quasi-homogeneous free divisor. These results are based on …

A complex hypersurface D in C n is a linear free divisor (LFD) if its module of logarithmic
vector fields has a global basis of linear vector fields. We classify all LFDs for n at most 4. By …

In this paper we prove that the Bernstein–Sato polynomial of any free divisor for which the D
[s]-module D [s] hs admits a Spencer logarithmic resolution satisfies the symmetry property b …

Dualité et comparaison pour les complexes de de Rham logarithmiques par rapport aux
diviseurs libres Page 1 ANNA L E S D E L’INSTITU T FO U RIER ANNALES DE L’INSTITUT …

In this article, we prove that a free divisor in a three-dimensional complex manifold must be
Euler homogeneous in a strong sense if the cohomology of its complement is the …

In this paper we survey the role of D-module theory in the comparison between logarithmic
and meromorphic de Rham complexes of integrable logarithmic connections with respect to …

This is a survey on our recent results on logarithmic vector fields and on holonomic D-
modules for algebraic local cohomology classes supported on hypersurfaces with isolated …