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Artículo
The module Dfs for locally quasi-homogeneous free divisors
(Springer, 2002-10)
We find explicit free resolutions for the D-modules Dfs and D[s]fs/D[s]f s+1, where f is a reduced equation of a locally quasi-homogeneous free divisor. These results are based on the fact that every locally quasi-homogeneous ...
Artículo
Algebraic computation of some intersection D-modules
(Springer, 2006)
Let X be a complex analytic manifold, D ⊂ X a locally quasi-homogeneous free divisor, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on X − D. In this ...
Artículo
Locally quasi-homogeneous free divisors are Koszul free
(MAIK Nauka/Interperiodica, 2002)
Let X be a complex analytic manifold and D ⊂ X be a free divisor. If D is locally quasi-homogeneous, then the logarithmic de Rham complex associated to D is quasi-isomorphic to Rj∗(CX\D), which is a perverse sheaf. On the ...
Artículo
Logarithmic cohomology of the complement of a plane curve
(Springer, 2002-03)
Let D, x be a plane curve germ. We prove that the complex Ω•(log D)x computes the cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial converse to a theorem of F.J. Castro-Jiménez, D. Mond ...
Artículo
On the logarithmic comparison theorem for integrable logarithmic connections
(London Mathematical Society, 2009)
Let 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 ...
Artículo
Dualité et comparaison sur les complexes de de Rham logarithmiques par rapport aux diviseurs libres
(Association des Annales de l'Institut Fourier, 2005)
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 ...