Correspondance d'Andreotti–Norguet et <em>D</em>-Modules

Abstract

We calculate the integral transform of a D-module of rank >1, locally free outside the zero section of the cotangent space to the complex projective space ℙ_n_. This allows us to complete some results of Andreotti–Norguet and Barlet: in particular we prove that the image of the integral transform obtained by integrating holomorphic forms along the linear cycles of ℙ_n_\ℙ_n-p_-1 (where 0 < p < n - 1), is the space of holomorphic functions on the variety of cycles Cp(ℙ_n_\ℙ_n-p_-1) which are annihilated by a family of differential operators of order four, that we determine explicitly.