The nonequivariant coherent-constructible correspondence for toric stacks

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.

v4: minor revision; 50 pages, some mistakes corrected

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Cited by in corpus (21)

• Mirror symmetry for very affine hypersurfaces
• Topological Fukaya category and mirror symmetry for punctured surfaces
• Sheaf quantization in Weinstein symplectic manifolds
• Resolutions of toric subvarieties by line bundles and applications
• Aspects of functoriality in homological mirror symmetry for toric varieties
• Rouquier dimension is Krull dimension for normal toric varieties
• Homological mirror symmetry at large volume
• Mirror symmetry for Berglund-Hübsch Milnor fibers
• Central charges of T-dual branes for toric varieties
• Categorical localization for the coherent-constructible correspondence
• Mirror Symmetry for Truncated Cluster Varieties
• Mirror symmetry for perverse schobers from birational geometry
• The circle quantum group and the infinite root stack of a curve (with an appendix by Tatsuki Kuwagaki)
• Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties
• Gamma II for toric varieties from integrals on T-dual branes and homological mirror symmetry
• Local mirror symmetry via SYZ
• Complex K-theory of mirror pairs
• Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces
• Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric Varieties
• Realizability in tropical geometry and unobstructedness of Lagrangian submanifolds
• Duality and kernels in microlocal geometry