Journal of Symplectic Geometry

Volume 21 (2023)

Number 2

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

Pages: 383 – 438

DOI: https://dx.doi.org/10.4310/JSG.2023.v21.n2.a4

Author

Ilaria Di Dedda (King’s College London, United Kingdom)

Abstract

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.

Received 5 April 2022

Received revised 26 September 2022

Accepted 2 October 2022

Published 28 September 2023