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arXiv · 1310.4866

Cohomology of abelian arrangements

Christin Bibby
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Abstract

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.

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Christin Bibby. 2013-10-17. Cohomology of abelian arrangements. https://doi.org/10.1090/proc/12937

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