Cohomology of abelian arrangements
An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. In this paper, we study the cohomology of the complement of an abelian arrangement. For unimodular abelian arrangements, we provide a combinatorial presentation for a differential graded algebra whose cohomology is isomorphic to the rational cohomology of the complement. Moreover, this DGA has a bi-grading that allows us to compute the mixed Hodge numbers.
Publication Source (Journal or Book title)
Proceedings of the American Mathematical Society
Bibby, C. (2016). Cohomology of abelian arrangements. Proceedings of the American Mathematical Society, 144 (7), 3093-3104. https://doi.org/10.1090/proc/12937