On the cohomology of arrangements of subtori

Abstract

Given an arrangement of subtori of arbitrary codimension in a torus, we compute the cohomology groups of the complement. Then, using the Leray spectral sequence, we describe the multiplicative structure on the graded cohomology. We also provide a differential model for the cohomology ring by considering a toric wonderful model and its Morgan algebra. Finally we focus on the divisorial case, proving a new presentation for the cohomology of toric arrangements.