Realising perfect derived categories of Auslander algebras of type $\mathbb{A}$ as Fukaya–Seidel categories

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 in [$\href{https://doi.org/10.1017/fms.2021.2}{9}$]. We provide a complete description of the Milnor fibre of such fibrations.

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Received 5 April 2022

Received revised 26 September 2022

Accepted 2 October 2022

Published 28 September 2023