Combinatorics and topology of toric arrangements defined by root systems
type: Item
instance of: scholarly article
title: Combinatorics and topology of toric arrangements defined by root systems
zbMATH Open document ID: 1194.14077
DOI: 10.4171/RLM/526
author: Luca Moci
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2010-09-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/0912.5458
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: Given the toric (or toral) arrangement defined by a root system \(\Phi\), we classify and count its components of each dimension. We show how to reduce to the case of 0-dimensional components, and in this case we give an explicit formula involving the maximal subdiagrams of the affine Dynkin diagram of \(\Phi\). Then we compute the Euler characteristic and the Poincaré polynomial of the complement of the arrangement, that is the set of regular points of the torus.
Mathematics Subject Classification ID: 14N10
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 20G20
zbMATH DE Number: 5787944
zbMATH Keywords: Dynkin
zbMATH Keywords: regular
zbMATH Keywords: root
zbMATH Keywords: torus
MaRDI profile type: Publication
arXiv ID: 0912.5458
cites work: Volume computation for polytopes and partition functions for classical root systems
cites work: Arrangement of hyperplanes. I: Rational functions and Jeffrey-Kirwan residue
cites work: Cohomology of affine Artin groups and applications
cites work: Q5668957
cites work: Q3375885
cites work: On the geometry of toric arrangements
cites work: A curious identity and the volume of the root spherical simplex. With an appendix by John R. Stembridge.
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description: scientific article