On the logarithmic comparison theorem for integrable logarithmic connections

2016-07-042016-07-042009Calderón Moreno, F.J. y Narváez Macarro, L. (2009). On the logarithmic comparison theorem for integrable logarithmic connections. Proceedings of the London Mathematical Society, 98 (3), 585-606.0024-61151460-244Xhttp://hdl.handle.net/11441/43095Let X be a complex analytic manifold, D ⊂ X a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), j : U = X − D ֒→ X the corresponding open inclusion, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on U. In this paper we prove that the canonical morphisms Ω • X(log D)(E(kD)) −→ Rj∗L, j!L −→ Ω • X(log D)(E(−kD)) are isomorphisms in the derived category of sheaves of complex vector spaces for k ≫ 0 (locally on X).application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/On the logarithmic comparison theorem for integrable logarithmic connectionsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttp://dx.doi.org/10.1112/plms/pdn043