Braid group actions on branched coverings and full exceptional sequences

Wen Chang; Fabian Haiden; Sibylle Schroll

doi:10.48550/arXiv.2301.04398

Braid group actions on branched coverings and full exceptional sequences

Wen Chang, Fabian Haiden, Sibylle Schroll

Publikation: Working paper › Forskning

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Abstrakt

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.

Originalsprog	Engelsk
Udgivelsessted	Cornell University
Udgiver	arXiv.org
Antal sider	1
DOI	https://doi.org/10.48550/arXiv.2301.04398
Status	Udgivet - 11. jan. 2023

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math.RT
math.AG
math.GT
math.RA

Dokumenter og links

10.48550/arXiv.2301.04398

2301.04398v1Forlagets udgivne version, 256 KB

Citationsformater

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N2 - 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.

AB - 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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Braid group actions on branched coverings and full exceptional sequences

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