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Direct image of logarithmic complexes and infinitesimal invariants of cycles

Morihiko Saito
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Abstract

We show that the direct image of the filtered logarithmic de Rham complex is a direct sum of filtered logarithmic complexes with coefficients in variations of Hodge structures, using a generalization of the decomposition theorem of Beilinson, Bernstein and Deligne to the case of filtered $D$-modules. The advantage of using the logarithmic complexes is that we have the strictness of the Hodge filtration by Deligne after taking the cohomology group in the projective case. As a corollary, we get the total infinitesimal invariant of a (higher) cycle in a direct sum of the cohomology of filtered logarithmic complexes with coefficients, and this is essentially equivalent to the cohomology class of the cycle.

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Morihiko Saito. 2005-08-31. Direct image of logarithmic complexes and infinitesimal invariants of cycles. https://arxiv.org/abs/math/0506020

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