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On the logarithmic comparison theorem for integrable logarithmic connections
Author(s) -
Calderón Moreno F. J.,
Narváez Macarro L.
Publication year - 2009
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdn043
Subject(s) - mathematics , algebra over a field , mathematics subject classification , combinatorics , pure mathematics
Let X be a complex analytic manifold, D ⊂ X a free divisor with jacobian ideal of linear type (for example, a locally quasi‐homogeneous free divisor), j : U = X − D ↪ X the corresponding open inclusion, ε an integrable logarithmic connection with respect to D and ℒ the local system of the horizontal sections of ε on U . In this paper we prove that the canonical morphisms Ω X • ( log D ) ( ε ( k D ) ) → R j * L , j ! L → Ω X • ( log D ) ( ε ( − k D ) ) are isomorphisms in the derived category of sheaves of complex vector spaces for k ≫ 0 (locally on X ).