Cohomology of abelian arrangements (Q2802126)

The configuration space of \(n\) points on an elliptic curve is an example of an abelian arrangement: a finite set of codimension one abelian subvarieties in a complex abelian variety. The author expands upon previous work on the study of cohomology of configuration spaces of smooth complex projective varieties as done independently by \textit{B. Totaro} [Topology 35, No. 4, 1057--1067 (1996; Zbl 0857.57025)] and \textit{I. Kříž} [Ann. Math. (2) 139, No. 2, 227--237 (1994; Zbl 0829.55008)]. In a similar fashion to the Orlik-Solomon algebra of an arrangement of hyperplanes, when the abelian arrangement is unimodular, the author provides a combinatorial presentation for a differential graded algebra whose cohomology is isomorphic to the rational cohomology of the complement.