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Clément Dupont
The Orlik-Solomon model for hypersurface arrangements
(Le modèle d’Orlik-Solomon pour les arrangements d’hypersurfaces)
Annales de l'institut Fourier, 65 no. 6 (2015), p. 2507-2545, doi: 10.5802/aif.2994
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Class. Math.: 14C30, 14F05, 14F25, 52C35
Keywords: arrangements, mixed Hodge theory, logarithmic forms, configuration spaces

Résumé - Abstract

We develop a model for the cohomology of the complement of a hypersurface arrangement inside a smooth projective complex variety. This generalizes the case of normal crossing divisors, discovered by P. Deligne in the context of the mixed Hodge theory of smooth complex varieties. Our model is a global version of the Orlik-Solomon algebra, which computes the cohomology of the complement of a union of hyperplanes in an affine space. The main tool is the complex of logarithmic forms along a hypersurface arrangement, and its weight filtration. Connections with wonderful compactifications and the configuration spaces of points on curves are also studied.

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