Cohomology of the complement to an elliptic arrangement

TL;DR

This paper studies the cohomology of the space obtained by removing an elliptic hyperplane arrangement, focusing on cases with nontrivial local systems, and provides new descriptions of its topological structure.

Contribution

It introduces a novel analysis of the cohomology of elliptic arrangements' complements with nontrivial local systems, extending previous hyperplane arrangement theories.

Findings

Explicit cohomology descriptions for elliptic arrangement complements

Analysis of local system coefficients in elliptic hyperplane arrangements

Extension of hyperplane arrangement cohomology to elliptic curves

Abstract

We consider the complement to an arrangement of hyperplanes in a cartesian power of an elliptic curve and describe its cohomology with coefficients in a nontrivial rank one local system.