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Realising perfect derived categories of Auslander algebras of type A as Fukaya-Seidel categories (2202.07024v3)
Published 14 Feb 2022 in math.SG and math.RT
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 by Dyckerhoff-Jasso-Lekili. We provide a complete description of the Milnor fibre of such fibrations.