Erratum to "The integer cohomology algebra of toric arrangements"

Filippo Callegaro, Emanuele Delucchi

Published 2019-10-30Version 1

We point out two errors in the paper "The integer cohomology algebra of toric arrangements, Advances in Mathematics, Vol. 313, pp.~746--802, 2017. The main error concerns Theorem 4.2.17. In particular the Diagram (8) does not commute in general. This invalidates the description for the ring structure of $H^*(M(\mathcal{A});\mathbb{Z})$ given in Theorem A and B. Still, under some restrictive hypotesis on $\mathcal{A}$ the results of Theorem 4.2.17 holds. We show a workaround to provide a description of the cohomology ring $H^*(M(\mathcal{A});\mathbb{Z})$ when $\mathcal{A}$ is a real complexified toric arrangement. The second error concerns the proof Theorem 7.2.1. The claim holds, but the proof is incorrect. We refer to a counterexample for the argument given in the proof and we provide references for a correct proof.