Braid group actions on branched coverings and full exceptional sequences
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917979874131968 |
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| author | Chang, Wen Haiden, Fabian Schroll, Sibylle |
| author_facet | Chang, Wen Haiden, Fabian Schroll, Sibylle |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04398 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Braid group actions on branched coverings and full exceptional sequences Chang, Wen Haiden, Fabian Schroll, Sibylle Representation Theory Algebraic Geometry Geometric Topology Rings and Algebras 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. |
| title | Braid group actions on branched coverings and full exceptional sequences |
| topic | Representation Theory Algebraic Geometry Geometric Topology Rings and Algebras |
| url | https://arxiv.org/abs/2301.04398 |