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G. Denham; H. Schenck; M. Schulze; M. Wakefield; U. Walther
Local cohomology of logarithmic forms
(Cohomologie locale des formes logarithmiques)
Annales de l'institut Fourier, 63 no. 3 (2013), p. 1177-1203, doi: 10.5802/aif.2787
Article PDF | Reviews MR 3137483 | Zbl 1277.32030
Class. Math.: 32S22, 52C35, 16W25
Keywords: hyperplane arrangement, logarithmic, differential form, free divisor

Résumé - Abstract

Let $Y$ be a divisor on a smooth algebraic variety $X$. We investigate the geometry of the Jacobian scheme of $Y$, homological invariants derived from logarithmic differential forms along $Y$, and their relationship with the property that $Y$ be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.

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