2004/11/30 by F. J. Calderon-Moreno, L. Narvaez-Macarro · 1 citation
Mathematics · #math.AG #msc:32C38 #msc:32S20 #msc:14F10
published as Annales de l'Institut Fourier 55, 1 (2005),47-75 · Final version
arxiv created 2005/05/18 · arxiv updated 2009/12/01
Let X be a complex analytic manifold and D ⊂ X a free divisor. Integrable logarithmic connections along D can be seen as locally free \cal OX-modules endowed with a (left) module structure over the ring of logarithmic differential operators \cal DX(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 DX and \cal DX(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.