Sur la transformation d'Abel–Radon de courants localement résiduels

Abstract

The aim of this Note is to give a generalisation of the following theorem of Henkin and Passare: let Y be an analytic subvariety of pure codimension p in a linearly p-concave domain U, and ω a meromorphic q-form ( q>0) on it; if the Abel–Radon transform A(ω∧[Y]) , which is meromorphic on U ∗ , has a meromorphic prolongation to U ∗ , then Y extends to an analytic subvariety of U , and ω to a meromorphic form on it. The problem is to show the analogous statement when we replace ω∧[ Y] by a current α of a more general type, called locally residual. We give the proof if α is of bidegree ( N,1), or ( q+1,1), 0< q< N in the particular case where A(α)=0 . We conclude with some applications of the theorem. To cite this article: B. Fabre, C. R. Acad. Sci. Paris, Ser. I 338 (2004).