2026/04/30 by Michela Barbieri, Andrew Hanlon, Jeff Hicks · 1 voice
Mathematics · #math.SG #math.AG
arxiv published 2026/04/30 · arxiv updated 2026/07/03
Mirror symmetry predicts an action by the fundamental group of a conjectural stringy Kähler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space is understood, but constructing the action is still an open problem in general. We propose that this action can be studied on the A-side via a moduli space of Legendrians isotopic to the FLTZ Legendrian. For the An-1 singularity, we construct an annular braid-group action on the corresponding partially wrapped Fukaya category by exact autoequivalences. The standard braid subgroup recovers the Seidel--Thomas action on the derived category, while the additional annular generator corresponds to tensor product with \mathcal O(-1). We additionally extend the Floer-theoretic approach to homological mirror symmetry for toric varieties to the setting of semiprojective toric Deligne--Mumford stacks over an arbitrary field.