Here we show that a Kupka component of a codimension 1 singular foliation of is a complete intersection. The result implies the existence of a meromorphic first integral of . The result was previously known if was assumed to be not a square.
To a germ with one-dimensional singular locus one associates series of isolated singularities , where l is a general linear function and . We prove an attaching result of Iomdin-Lê type which compares the homotopy types of the Milnor fibres of and f. This is a refinement of the Iomdin-Lê theorem in the general setting of a singular underlying space.
In this survey we give geometric interpretations of some standard results on boundary behaviour of holomorphic self-maps in the unit disc of ℂ and generalize them to holomorphic self-maps of some particular domains of ℂⁿ.
Let be a Hermitian symmetric space of tube type, its Silov boundary and the neutral component of the group of bi-holomorphic diffeomorphisms of . Our main interest is in studying the action of on . Sections 1 and 2 are part of a joint work with B. Ørsted (see [4]). In Section 1, as a pedagogical introduction, we study the case where is the unit disc and is the circle. This is a fairly elementary and explicit case, where one can easily get a flavour of the more general results. In Section...
We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
We extend the theory of separately holomorphic mappings between complex analytic spaces. Our method is based on Poletsky theory of discs, Rosay theorem on holomorphic discs and our recent joint-work with Pflug on boundary cross theorems in dimension It also relies on our new technique of conformal mappings and a generalization of Siciak’s relative extremal function. Our approach illustrates the unified character: “From local information to global extensions”. Moreover, it avoids systematically...