Realising perfect derived categories of Auslander algebras of type A as Fukaya-Seidel categories
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911467776770048 |
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| author | Di Dedda, Ilaria |
| author_facet | Di Dedda, Ilaria |
| contents | We prove that the Fukaya-Seidel categories of a certain family of Lefschetz fibrations on $\mathbb{C}^2$ are equivalent to the perfect derived categories of Auslander algebras of Dynkin type $\mathbb{A}$. We give an explicit equivalence between these categories and the partially wrapped Fukaya categories considered by Dyckerhoff-Jasso-Lekili. We provide a complete description of the Milnor fibre of such fibrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07024 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Realising perfect derived categories of Auslander algebras of type A as Fukaya-Seidel categories Di Dedda, Ilaria Symplectic Geometry Representation Theory We prove that the Fukaya-Seidel categories of a certain family of Lefschetz fibrations on $\mathbb{C}^2$ are equivalent to the perfect derived categories of Auslander algebras of Dynkin type $\mathbb{A}$. We give an explicit equivalence between these categories and the partially wrapped Fukaya categories considered by Dyckerhoff-Jasso-Lekili. We provide a complete description of the Milnor fibre of such fibrations. |
| title | Realising perfect derived categories of Auslander algebras of type A as Fukaya-Seidel categories |
| topic | Symplectic Geometry Representation Theory |
| url | https://arxiv.org/abs/2202.07024 |