Positivity Notions for Coherent Sheaves over Compact Complex Spaces.
Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations
It is a known fact that the space of codimension one holomorphic foliations with singularities with a given ‘normal bundle’ has a natural structure of an algebraic variety. The aim of this paper is to consider the problem of the description of its irreducible components. To do this, we are interested in the problem of the existence of an integral factor of a twisted integrable differential 1–form defined on a projective manifold. We are going to do a geometrical analysis of the codimension one foliation...
Potential theory and several complex variables
Potentials in pluripotential theory
Potentials with respect to the pluricomplex Green function
For μ a positive measure, we estimate the pluricomplex potential of μ, , where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.
Power series with integer coefficients in several variables.
Precise regularity up to the boundary of proper holomorphic mappings
Premiers pas en calcul étranger
Cet exposé est une introduction au calcul étranger d’Écalle, c’est-à-dire au calcul des obstructions à la sommabilité de Borel d’une grande classe de séries formelles, les fonctions résurgentes d’Écalle. La théorie d’Écalle éclaire d’un jour neuf le célèbre phénomène de Stokes qui est illustré ici dans le contexte de la méthode du col.
Préparation des fonctions sous-analytiques globales et lieu d'analyticité
We give a new proof of Kurdyka-Tamm's theorem on the analytic locus of a subanalytic function.
Preparation theorems for matrix valued functions
We generalize the Malgrange preparation theorem to matrix valued functions satisfying the condition that vanishes to finite order at . Then we can factor near (0,0), where is inversible and is polynomial function of depending on . The preparation is (essentially) unique, up to functions vanishing to infinite order at , if we impose some additional conditions on . We also have a generalization of the division theorem, and analytic versions generalizing the Weierstrass preparation...
Primitive elements in rings of holomorphic functions.
Primitive Holomorphic Maps of Curves.
Principal bundles with parabolic structure.
Principal Orbit Types for Reductive Groups Acting on Stein Manifolds.
Principe de Boyarsky et ...-modules.
Principe d'Oka-Grauert dans A?.
Principe du maximum et théorème de Lubin-Hensel dans
Privilege on strictly convex domains
We adapt the privilege theorem of Douady and Pourcin from polydomains to strictly convex domains in the complex space.
Problème de Cauchy microdifférentiel
Problème de Cauchy pour les hyperfonctions à croissance