Interpolating discrete multiplicity varieties for
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
Intersection theory in complex analytic geometry
We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.
Le problème de Riemann Hilbert sur une variété analytique complexe
Le problème de Riemann Hilbert sur une variété analytique complexe
Le problème de Riemann-Hilbert sur une variété complexe s’énonce de la manière suivante : soit un sous-ensemble analytique de de codimension un en chacun de ses points et une représentation de dans . Existe-t-il un système de Pfaff du type de Fuchs où (J. de Math. Pures et Appl., 47, (1968)) dont la monodromie soit la classe de la représentation ?On montre en particulier que si est une variété de Stein contractile et si les composantes irréductibles de sont sans singularités...
Le reseau L2 d'un Systeme holonome regulier.
Liouville-type theorems for foliations with complex leaves
In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds of , in particular Levi flat ones. As a general scheme, we suppose that is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.
Lipschitz equisingularity [Book]
Local Complex Foliation of Real Submanifolds.
Local Homological Properties of Analytic Sets.
Minimal equations, global reducibility of holomorphic functions, and relative rationality of analytic sets
Minimal Varieties and Harmonic Maps in Tori.
Non-analytic Hypersurfaces in Cn.
On a Generalization of the Hopf Fibration, III. (Subvarieties in the C-Spaces).
On complete intersections
We construct closed complex submanifolds of which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of .
On Dolbeault Cohomology and Envelopes of Holomorphy.
On improper isolated intersection in complex analytic geometry
On irreducible components of a Weierstrass-type variety
We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.
On Noether and strict stability, Hilbert exponent, and relative Nullstellensatz
Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in , respectively, . Also...
On proper discs in complex manifolds
Let be a complex manifold of dimension at least which has an exhaustion function whose Levi form has at each point at least strictly positive eigenvalues. We construct proper holomorphic discs in through any given point and in any given direction.
On the compactification problem for Stein surfaces