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.
OriginalsprogEngelsk
Publikationsdato11. jan. 2023
UdgivelsesstedCornell University
UdgiverarXiv.org
Antal sider17
DOI
StatusUdgivet - 11. jan. 2023

Emneord

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

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