A calculus for meromorphic currents.
A special integral representation for a local residue.
Adeles and differential forms.
Algebraic Cycles as Residues of Meromorphic Forms.
An expression for the superposition of general algebraic functions in terms of hypergeometric series.
Analytic Continuation of Currents and Division Problems.
Binomial residues
A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of -hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with .
Calcul des résidus en analyse -adique
Coleff-Herrera currents, duality, and noetherian operators
Let be a coherent subsheaf of a locally free sheaf and suppose that has pure codimension. Starting with a residue current obtained from a locally free resolution of we construct a vector-valued Coleff-Herrera current with support on the variety associated to such that is in if and only if . Such a current can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction...
Der Residuenkomplex in der lokalen algebraischen und analytischen Geometrie.
Diagonals of the Laurent series of rational functions.
Extension et division dans les variétés à croisements normaux.
Let D be a bounded strictly pseudoconvex domain with smooth boundary and f = (f1, ..., fp) (fi ∈ Hol(D)) a complete intersection with normal crossing. In this paper we study an extension problem in L∞-norm for holomorphic functions defined on f-1(0) ∩ D and a decomposition formula g = ∑i=1p figi for holomorphic functions g ∈ I(f1, ..., fp)(D) in Lipschitz spaces. We stress that for the two problems the classical theorem cannot be applied because f-1(0) has singularities on the boundary ∂D. This...
Formules de Jacobi et méthodes analytiques
On se propose de retrouver, via des méthodes d'inspiration analytiques basées sur l'utilisation de formules de représentation intégrale attachées à des applications holomorphes propres d'un ouvert de ℂⁿ dans ℂⁿ, les formules de Jacobi généralisées obtenues par C. A. Berenstein, A. Vidras et A. Yger; le fait de disposer de telles preuves (basées sur un raisonnement limité au cadre strictement affine et ne nécessitant pas le recours à une compactification) autorise l'extension de ces résultats au...
Ind-Sheaves, distributions, and microlocalization
Integral transforms for divisors in and solutions of systems of PDE’s
Meromorphic functions and analytic cycles. (Fonctions méromorphes et cycles analytiques.)
Multidimensional residues and ideal membership.
Let I(f) be a zero-dimensional ideal in C[z1, ..., zn] defined by a mapping f. We compute the logarithmic residue of a polynomial g with respect to f. We adapt an idea introduced by Aizenberg to reduce the computation to a special case by means of a limiting process.We then consider the total sum of local residues of g w.r.t. f. If the zeroes of f are simple, this sum can be computed from a finite number of logarithmic residues. In the general case, you have to perturb the mapping f. Some applications...
On Bochner-Martinelli residue currents and their annihilator ideals
We study the residue current of Bochner-Martinelli type associated with a tuple of holomorphic germs at , whose common zero set equals the origin. Our main results are a geometric description of in terms of the Rees valuations associated with the ideal generated by and a characterization of when the annihilator ideal of equals .
On some generalizations of Jacobi's residue formula
On the Briançon-Skoda theorem on a singular variety
Let be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.