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VOL. 62 | 2012 Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements
Graham Denham, Mathias Schulze

Editor(s) Hiroaki Terao, Sergey Yuzvinsky

Abstract

We describe dualities and complexes of logarithmic forms and differentials for central affine and corresponding projective arrangements. We generalize the Borel–Serre formula from vector bundles to sheaves on $\mathbb{P}^d$ with locally free resolutions of length one. Combining these results we present a generalization of a formula due to Mustaţă and Schenck, relating the Poincaré polynomial of an arrangement in $\mathbb{P}^3$ (or a locally tame arrangement in $\mathbb{P}^d$ with zero-dimensional non-free locus) to the total Chern polynomial of its sheaf of logarithmic 1-forms.

Information

Published: 1 January 2012
First available in Project Euclid: 24 November 2018

zbMATH: 1258.32009
MathSciNet: MR2933791

Digital Object Identifier: 10.2969/aspm/06210027

Subjects:
Primary: 16W25, 32S22, 52C35

Rights: Copyright © 2012 Mathematical Society of Japan

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