Coherent-Constructible Correspondence for Toric Fibrations

2023/04/03 by Yuxuan Hu, Hu, Yuxuan, Pyongwon Suh +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2304.00832

openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Σ be a fan inside the lattice ℤⁿ, and E:ℤⁿ → PicS be a map of abelian groups. We introduce the notion of a principal toric fibration X_{Σ, E} over the base scheme S, relativizing the usual toric construction for Σ. We show that the category of ind-coherent sheaves on such a fibration is equivalent to the global section of the Kashiwara-Schapira stack twisted by a certain local system of categories with stalk IndCoh S. It is a simultaneous generalization of the work of Harder-Katzarkov [HK19] and of Kuwagaki [Kuw20], and should be seen as a family-version of the coherent-constructible correspondence [FLTZ11].

Related

• Functoriality of toric coherent-constructible correspondence
• Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric Varieties
• The nonequivariant coherent-constructible correspondence and tilting
• Coherent sheaves, sheared D-modules, and Hochschild cochains
• Remarks on the nonequivariant coherent-constructible correspondence for toric varieties