A Vanishing Theorem for Power Series.
A weak invertibility criterion in the weighted -spaces of holomorphic functions in the ball.
About the derivatives of Cauchy type integrals in the polydisc.
Accelero-summation of the formal solutions of nonlinear difference equations
In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level ”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...
Addendum to My Paper "Algebraic Values of Meromorphic Maps".
Addendum to the paper : “Formal cohomology, analytic cohomology and non-algebraic manifolds”
Adeles and differential forms.
Algebraic Cycles as Residues of Meromorphic Forms.
Algebraic dependences of meromorphic mappings sharing few moving hyperplanes
We study algebraic dependences of three meromorphic mappings which share few moving hyperplanes without counting multiplicity.
Algebraic dimension of twistor spaces and scalar curvature of anti-self-dual metrics.
Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions.
Algebraic tubular neighbourhoods I.
Algebraic tubular neighbourhoods II.
Algebraic Values of Meromorphic Maps
Algorithme de calcul du polynôme de Bernstein : Cas non dégénéré
Nous commençons par indiquer comment la connaissance du degré d’un opérateur différentiel, unitaire en et annulant , permet de donner un algorithme de calcul du polynôme de Bernstein d’un germe de fonction analytique à singularité isolée.Nous étudions alors le cas d’une singularité non dégénérée par rapport à son polygôme de Newton; nous donnons un algorithme pour calculer le polynôme de Bernstein de ces singularités et l’équation fonctionnelle associée. Notre méthode utilise une filtration...
Amibes de variétés algébriques et dénombrement de courbes
Les amibesdes variétés algébriques dans sont les images de ces variétés par l’application des moments , . Des résultats obtenus par G. Mikhalkin montrent l’utilité des amibes pour l’étude des variétés algébriques réelles et complexes. Les amibes peuvent être déformées en des complexes polyédraux appelésvariétés algébriques tropicales. Cette déformation permet, en particulier, de calculer les invariants de Gromov-Witten du plan projectif et d’autres surfaces toriques en dénombrant des courbes...
An analog of the Fubini-Studi form for two-dimensional toric varieties.
An analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function
We derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula satisfied by Herglotz-Nevanlinna and Cauchy-type functions. We also provide an extension of the Stieltjes inversion formula for Cauchy-type and quasi-Cauchy-type functions.
An Approximate Riemann Mapping Theorem in Cn.
An elementary proof of the Briançon-Skoda theorem
We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function belongs to an ideal of the ring of germs of analytic functions at ; more precisely, the ideal membership is obtained if a function associated with and is locally square integrable. If can be generated by elements,it follows in particular that , where denotes the integral closure of an ideal .