On the cohomology of arrangements of subtori
arXiv:2001.05180 · doi:10.1112/jlms.12616
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.
25 pages. In this version a new Section was added, containing a presentation for the cohomology ring of toric arrangements. Furthermore the other sections were expanded to improve readability