We point out two errors in the paper "The integer cohomology algebra of toric arrangements" Adv. Math. 313 (2017). 746--802. The main error concerns Theorem 4.2.17. In that theorem’s proof, Diagram (8) does not commute in general but only under some restrictive hypotheses on the arrangement A. This invalidates the description for the ring structure of H ∗ (M (A); Z) given in Theorems A and B. We refer to alternative descriptions of the cohomology ring H ∗ (M (A); Z). The second error concerns 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 provide references to a correct proof.
Corrigendum to “The integer cohomology algebra of toric arrangements” [Adv. Math. 313 (2017) 746–802]
Callegaro, Filippo
Co-primo
;
2025-01-01
Abstract
We point out two errors in the paper "The integer cohomology algebra of toric arrangements" Adv. Math. 313 (2017). 746--802. The main error concerns Theorem 4.2.17. In that theorem’s proof, Diagram (8) does not commute in general but only under some restrictive hypotheses on the arrangement A. This invalidates the description for the ring structure of H ∗ (M (A); Z) given in Theorems A and B. We refer to alternative descriptions of the cohomology ring H ∗ (M (A); Z). The second error concerns 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 provide references to a correct proof.| File | Dimensione | Formato | |
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