Symplectic higher Auslander correspondence for type A
Abstract
We prove that the Fukaya-Seidel categories of a certain family of singularities on are equivalent to the perfect derived categories of higher Auslander algebras of Dynkin type A. We relate these to the Fukaya-Seidel categories of Brieskorn-Pham singularities and to the partially wrapped Fukaya categories considered by Dyckerhoff-Jasso-Lekili. We provide a symplectic interpretation to higher Auslander correspondence of type A in terms of Fukaya-Seidel categories of Lefschetz fibrations.
Cite
@article{arxiv.2311.16859,
title = {Symplectic higher Auslander correspondence for type A},
author = {Ilaria Di Dedda},
journal= {arXiv preprint arXiv:2311.16859},
year = {2026}
}
Comments
67 pages, 22 figures. (v3) Incorporated referee comments and thesis corrections. Fixed gap in proof of Proposition 3.16 (now 3.45). Added new section comparing $f_{n,d}$ and $\Phi_{n,d}$. Expanded arguments, improved exposition, minor changes throughout. Accepted version, to appear in Quantum Topology