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Peer-reviewedCC BY 4.0Forum of Mathematics, Sigma

Monodromy of supersolvable toric arrangements

  • Christin Bibby1
  • Daniel C. Cohen1
  • Emanuele Delucchi2
  1. 1Louisiana State University
  2. 2University of Applied Arts and Sciences of Southern Switzerland
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Abstract

We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and bundles involving classical configuration spaces. In the toric case, we show that the monodromy of a supersolvable arrangement bundle factors through the Artin braid group, and that of a strictly supersolvable arrangement bundle factors further through the Artin pure braid group. The latter factorization is particularly informative – we use it to determine a number of invariants of the complement of a strictly supersolvable arrangement, including the cohomology ring and the lower central series Lie algebra of the fundamental group.

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Cite

BibTeXRIS
BibTeX
@article{bibby2026monodromy,
  title = {{Monodromy of supersolvable toric arrangements}},
  author = {Christin Bibby and Daniel C. Cohen and Emanuele Delucchi},
  journal = {Forum of Mathematics, Sigma},
  year = {2026},
  month = nov,
  doi = {10.1017/fms.2026.10280},
  url = {https://www.cambridge.org/core/product/identifier/S2050509426102801/type/journal_article},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Monodromy of supersolvable toric arrangements
AU  - Christin Bibby
AU  - Daniel C. Cohen
AU  - Emanuele Delucchi
PY  - 2026
DA  - 2026/11/06
JO  - Forum of Mathematics, Sigma
DO  - 10.1017/fms.2026.10280
UR  - https://www.cambridge.org/core/product/identifier/S2050509426102801/type/journal_article
AB  - We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and bundles involving classical configuration spaces. In the toric case, we show that the monodromy of a supersolvable arrangement bundle factors through the Artin braid group, and that of a strictly supersolvable arrangement bundle factors further through the Artin pure braid group. The latter factorization is particularly informative – we use it to determine a number of invariants of the complement of a strictly supersolvable arrangement, including the cohomology ring and the lower central series Lie algebra of the fundamental group.
SN  - 2050-5094
ER  -