The integer cohomology algebra of toric arrangements

Filippo Callegaro; Emanuele Delucchi

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arXiv · 1504.06169

The integer cohomology algebra of toric arrangements

Filippo Callegaro·Emanuele Delucchi

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Abstract

We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data. To this end, we study a morphism of spectral sequences associated to certain combinatorially defined subcomplexes of the toric Salvetti category in the complexified case, and use a technical argument in order to extend the results to full generality. As a byproduct we obtain: -a "combinatorial" version of Brieskorn's lemma in terms of Salvetti complexes of complexified arrangements, -a uniqueness result for realizations of arithmetic matroids with at least one basis of multiplicity 1.

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Filippo Callegaro, Emanuele Delucchi. 2015-04-23. The integer cohomology algebra of toric arrangements. https://arxiv.org/abs/1504.06169

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