Braid group actions on branched coverings and full exceptional sequences
Representation Theory
2025-04-09 v3 Algebraic Geometry
Geometric Topology
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2301.04398,
title = {Braid group actions on branched coverings and full exceptional sequences},
author = {Wen Chang and Fabian Haiden and Sibylle Schroll},
journal= {arXiv preprint arXiv:2301.04398},
year = {2025}
}
Comments
v3: improvements to exposition based on referee comments. To appear in Adv. Math