English

Symplectic higher Auslander correspondence for type A

Symplectic Geometry 2026-02-26 v3 Representation Theory

Abstract

We prove that the Fukaya-Seidel categories of a certain family of singularities on Cd\mathbb{C}^d 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

R2 v1 2026-06-28T13:34:15.303Z