English

Mirror symmetry for honeycombs

Symplectic Geometry 2019-11-06 v3 Algebraic Geometry

Abstract

We prove a homological mirror symmetry equivalence between an AA-brane category for the pair of pants, computed as a wrapped microlocal sheaf category, and a BB-brane category for a mirror LG model, understood as a category of matrix factorizations. The equivalence improves upon prior results in two ways: it intertwines evident affine Weyl group symmetries on both sides, and it exhibits the relation of wrapped microlocal sheaves along different types of Lagrangian skeleta for the same hypersurface. The equivalence proceeds through the construction of a combinatorial realization of the AA-model via arboreal singularities. The constructions here represent the start of a program to generalize to higher dimensions many of the structures which have appeared in topological approaches to Fukaya categories of surfaces.

Keywords

Cite

@article{arxiv.1702.03255,
  title  = {Mirror symmetry for honeycombs},
  author = {Benjamin Gammage and David Nadler},
  journal= {arXiv preprint arXiv:1702.03255},
  year   = {2019}
}

Comments

v3: Minor edits throughout; to appear in Trans. AMS

R2 v1 2026-06-22T18:15:07.081Z