# Cohomology of the complement of an elliptic arrangement

In the paper "Cohomology of the complement of an elliptic arrangement", the authors (Levin and Varchenko) consider the complement to an arrangement of (elliptic) hyperplanes in a cartesian power of an elliptic curve and describe its cohomology with coefficients in a non-trivial rank one local system (Actually, their result concerns generic rank one local systems).

What about the case of the trivial rank one local system $\mathbb C$?

I'm mainly interested in the case of the square of an elliptic curve. Maybe this is already known. In this case, a good reference would be welcome