Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements

Graham Denham; Mathias Schulze

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arXiv · 1004.4237

Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements

Graham Denham·Mathias Schulze

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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 projective d-space with locally free resolutions of length one. Combining these results we present a generalization of a formula due to Mustata and Schenck, relating the Poincare polynomial of an arrangement in projective 3-space (or a locally tame arrangement in projective d-space with zero-dimensional non-free locus) to the total Chern polynomial of its sheaf of logarithmic 1-forms.

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Graham Denham, Mathias Schulze. 2010-04-23. Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements. https://arxiv.org/abs/1004.4237

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