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Transactions of the American Mathematical Society

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Corrigendum to ``Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements''


Authors: Filippo Callegaro, Michele D’Adderio, Emanuele Delucchi, Luca Migliorini and Roberto Pagaria
Journal: Trans. Amer. Math. Soc. 374 (2021), 3779-3781
MSC (2020): Primary 14N20, 52C35, 55R80
DOI: https://doi.org/10.1090/tran/8262
Published electronically: February 17, 2021
Original Article: Trans. Amer. Math. Soc. 373 (2020), 1909-1940.
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Abstract: In this short note we correct the statement of the main result of [Trans. Amer. Math. Soc. 373 (2020), no. 3, 1909-1940]. That paper presented the rational cohomology ring of a toric arrangement by generators and relations. One of the series of relations given in the paper is indexed over the set circuits in the arrangement's arithmetic matroid. That series of relations should however be indexed over all sets $ X$ with $ \lvert X \rvert =\operatorname {rk}(X)+1$. Below we give the complete and correct presentation of the rational cohomology ring.


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Additional Information

Filippo Callegaro
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Email: callegaro@dm.unipi.it

Michele D’Adderio
Affiliation: Département de Mathématique, Université Libre de Bruxelles (ULB), Boulevard du Triomphe, B-1050 Bruxelles, Belgium
Email: mdadderi@ulb.ac.be

Emanuele Delucchi
Affiliation: Département de mathématiques, Université de Fribourg, Chemin du Musée 23, CH-1700 Fribourg, Switzerland
Email: emanuele.delucchi@unifr.ch

Luca Migliorini
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
Email: luca.migliorini@unibo.it

Roberto Pagaria
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
Email: roberto.pagaria@unibo.it

DOI: https://doi.org/10.1090/tran/8262
Received by editor(s): January 22, 2020
Received by editor(s) in revised form: July 22, 2020
Published electronically: February 17, 2021
Additional Notes: The first and fourth authors were supported by PRIN 2015 “Moduli spaces and Lie theory” 2015ZWST2C - PE1.
The third author was supported by the Swiss National Science Foundation professorship grant PP00P2_150552/1.
Article copyright: © Copyright 2021 American Mathematical Society