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

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

2004-11-02

arxiv.org/abs/math/0411045v2

Annales de l'Institut Fourier 55, 1 (2005),47-75

Mathematics

Algebraic Geometry

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Scientific paper

Let X be a complex analytic manifold and D \subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {\cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic differential operators {\cal D}_X(\log D). In this paper we study two related results: the relationship between the duals of any integrable logarithmic connection over the base rings {\cal D}_X and {\cal D}_X(\log D), 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.

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