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

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

2010-04-23

arxiv.org/abs/1004.4237v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

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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