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Cohomology of complements of toric arrangements associated with root systems

Authors
  • Bergvall, Olof1
  • 1 University of Gävle, Gävle, Sweden , Gävle (Sweden)
Type
Published Article
Journal
Research in the Mathematical Sciences
Publisher
Springer International Publishing
Publication Date
Jan 09, 2022
Volume
9
Issue
1
Identifiers
DOI: 10.1007/s40687-021-00305-z
Source
Springer Nature
Keywords
Disciplines
  • Research
License
Green

Abstract

We develop an algorithm for computing the cohomology of complements of toric arrangements. In the case a finite group Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} is acting on the arrangement, the algorithm determines the cohomology groups as representations of Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}. As an important application, we determine the cohomology groups of the complements of the toric arrangements associated with root systems of exceptional type as representations of the corresponding Weyl groups.

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