Dualité et comparaison pour les complexes de de Rham logarithmiques par rapport aux diviseurs libres

Abstract

Let X be a complex analytic manifold and D⊂X a free divisor. Integrable logarithmic connections along D can be seen as locally free 𝒪 X -modules endowed with a (left) module structure over the ring of logarithmic differential operators 𝒟 X (logD). In this paper we study two related results: the relationship between the duals of any integrable logarithmic connection over the base rings 𝒟 X and 𝒟 X (logD), and a differential criterion for the logarithmic comparison theorem. We also generalize a formula of Esnault-Viehweg in the normal crossing case for the Verdier dual of a logarithmic de Rham complex.