Let D be the germ of a reduced hypersurface in (Cn, 0) defined by f∈ C {x}:= C {x1,..., xn}
and with ring OD= C {x}/(f). In his fundamental paper [28], K. Saito introduces the notions of …

In this paper we compare different notions of transversality for possible singular complex
algebraic or analytic subsets of an ambient complex manifold and prove a refined …

We obtain several new characterizations of splayedness for divisors: a Leibniz property for
ideals of singularity subschemes, the vanishing of a 'splayedness' module, and the …

Kyoji Saito defined a residue map from the logarithmic differential 1-forms along a reduced
complex analytic hypersurface to the meromorphic functions on the hypersurface. He …

La théorie des champs de vecteurs logarithmiques et des formes différentielles
logarithmiques d'une hypersurface singulière réduite est développée par K. Saito. Ces …

We generalize the Chern class relation for the transversal intersection of two nonsingular
varieties to a relation for possibly singular varieties, under a splayedness assumption. We …

The objective of this article is to give an effective algebraic characterization of normal
crossing hypersurfaces in complex manifolds. It is shown that a divisor (= hypersurface) has …

We introduce two families of ideals, F-jumping ideals and F-Jacobian ideals, in order to
study the singularities of hypersurfaces in positive characteristic. Both families are defined …

Abstract A collection A={D 1,…, D n} of divisors on a smooth variety X is an arrangement if
the intersection of every subset of A is smooth. We show that, if X is defined over a field of …

Let $ X $ be a nonsingular complex projective variety and $ D $ a locally quasi-
homogeneous free divisor in $ X $. In this paper we study a numerical relation between the …