Journal article

Orlik-Solomon type presentations for the cohomology algebra of toric arrangements

  • Callegaro, Filippo Dipartimento di Matematica, Universitá di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italia
  • D’Adderio, Michele Département de Mathématique, Université Libre de Bruxelles (ULB), Boulevard du Triomphe, B-1050 Bruxelles, Belgium
  • Delucchi, Emanuele Département de mathématiques, Université de Fribourg, Chemin du Musée 23, CH-1700 Fribourg, Switzerland
  • Migliorini, Luca Dipartimento di Matematica, Universitá di Bologna, Piazza di Porta S. Donato 5, Bologna, Italia
  • Pagaria, Roberto Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italia
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    12.11.2019
Published in:
  • Transactions of the American Mathematical Society. - 2019, vol. 373, no. 3, p. 1909–1940
English We give an explicit presentation for the integral cohomology ring of the complement of any arrangement of level sets of characters in a complex torus (alias ``toric arrangement''). Our description parallels the one given by Orlik and Solomon for arrangements of hyperplanes and builds on De Concini and Procesi's work on the rational cohomology of unimodular toric arrangements. As a byproduct we extend Dupont's rational formality result to formality over $ \mathbb{Z}$.The data needed in order to state the presentation of the rational cohomology is fully encoded in the poset of connected components of intersections of the arrangement.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/308552
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