The integer cohomology algebra of toric arrangements
- Callegaro, Filippo Dipartimento di Matematica, University of Pisa, Italy
- Delucchi, Emanuele Departement de mathématiques, Université de Fribourg, Switzerland
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20.06.2017
Published in:
- Advances in Mathematics. - 2017, vol. 313, p. 746–802
Toric arrangements
Hyperplane arrangements
Cell complexes
Posets
Small categories without loops
Combinatorial topology
Orlik–Solomon algebra
Salvetti complex
Arithmetic matroids
English
We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data. To this end, we study a morphism of spectral sequences associated to certain combinatorially defined subcomplexes of the toric Salvetti category in the complexified case, and use a technical argument in order to extend the results to full generality. As a byproduct we obtain:– a “combinatorial” version of Brieskorn's lemma in terms of Salvetti complexes of complexified arrangements,– a uniqueness result for realizations of arithmetic matroids with at least one basis of multiplicity 1
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 305084
- DOI 10.1016/j.aim.2017.04.017
- Persistent URL
- https://folia.unifr.ch/unifr/documents/306107
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