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Proceedings of the London Mathematical Society Advance Access originally published online on October 29, 2008
Proceedings of the London Mathematical Society 2009 98(3):585-606; doi:10.1112/plms/pdn043
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© 2008 London Mathematical Society

On the logarithmic comparison theorem for integrable logarithmic connections

F. J. Calderón Moreno and L. Narváez Macarro

Departamento de Álgebra
Facultad de Matemáticas
Universidad de Sevilla
PO Box 1160
41080 Sevilla
Spain
narvaez@algebra.us.es

Received 12 June 2007. Revision received 10 July 2008.

Let X be a complex analytic manifold, D sub X a free divisor with jacobian ideal of linear type (for example, a locally quasi-homogeneous free divisor), j: U = X – D {rightarrowhook} X the corresponding open inclusion, {varepsilon} an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of {varepsilon} on U. In this paper we prove that the canonical morphisms Formula are isomorphisms in the derived category of sheaves of complex vector spaces for k >> 0 (locally on X).

2000 Mathematics Subject Classification 32C38, 14F40, 32S40.

The authors are partially supported by MTM2004-07203-C02-01 and FEDER.


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