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arXiv · 2301.04398

Braid group actions on branched coverings and full exceptional sequences

Wen Chang·Fabian Haiden·Sibylle Schroll
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Abstract

We relate full exceptional sequences in Fukaya categories of surfaces or equivalently in derived categories of graded gentle algebras to branched coverings over the disk, building on a previous classification result of the first and third author. This allows us to apply tools from the theory of branched coverings such as Birman--Hilden theory and Hurwitz systems to study the natural braid group action on exceptional sequences. As an application, counterexamples are given to a conjecture of Bondal--Polishchuk on the transitivity of the braid group action on full exceptional sequences in a triangulated category.

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Wen Chang, Fabian Haiden, Sibylle Schroll. 2025-04-08. Braid group actions on branched coverings and full exceptional sequences. https://arxiv.org/abs/2301.04398

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