On the logarithmic comparison theorem for integrable logarithmic connections

Abstract

Let $X$ be a complex analytic manifold, $D\subset X$ a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), $j:U=X-D\to X$ 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 between the logarithmic de Rham complex of $E(kD)$ and $R{j}_{\ast }L$ (resp. the logarithmic de Rham complex of $E(-kD)$ and $j_{!}L$) are isomorphisms in the derived category of sheaves of complex vector spaces for $k\gg 0$ (locally on $X$)

Terminology has changed: "linear jacobian type" instead of "commutative differential type"); no Koszul hypothesis is needed in theorem (2.1.1); minor changes. To appear in Proc. London Math. Soc

References in corpus (1)

• Free divisors and duality for D-modules

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• A vanishing theorem for a class of logarithmic D-modules
• Hodge ideals of free divisors
• Tautological systems and free divisors
• On strong Euler-homogeneity and Saito-holonomicity for complex hypersurfaces. Applications to a conjecture on free divisors