The integer cohomology algebra of toric arrangements

Callegaro, Filippo and Delucchi, Emanuele (2017) The integer cohomology algebra of toric arrangements. Advances in Mathematics, 313. pp. 746-802. ISSN 00018708

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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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