The nonequivariant coherent-constructible correspondence for toric stacks

TL;DR

This paper extends the microlocal-geometric interpretation of homological mirror symmetry from toric varieties to a broader class of toric stacks, including orbifolds, using gluing techniques for $$-categories.

Contribution

It generalizes the nonequivariant coherent-constructible correspondence to toric stacks, broadening the scope of the conjecture and its geometric understanding.

Findings

Proves the correspondence for a class of toric stacks including orbifolds.

Uses gluing descriptions of $$-categories for both sides of the correspondence.

Establishes a unified framework for understanding homological mirror symmetry in toric geometry.

Abstract

The nonequivariant coherent-costructible correspondence is a microlocal-geometric interpretation of homological mirror symmetry for toric varieties conjectured by Fang-Liu-Treumann-Zaslow. We prove a generalization of this conjecture for a class of toric stacks which includes any toric varieties and toric orbifolds. Our proof is based on gluing descriptions of $\infty$-categories of both sides.