Monodromy of supersolvable toric arrangements

Christin Bibby; Daniel C. Cohen; Emanuele Delucchi

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arXiv · 2510.00166

Monodromy of supersolvable toric arrangements

Christin Bibby·Daniel C. Cohen·Emanuele Delucchi

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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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Christin Bibby, Daniel C. Cohen, Emanuele Delucchi. 2025-09-30. Monodromy of supersolvable toric arrangements. https://arxiv.org/abs/2510.00166

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