Functoriality of toric coherent-constructible correspondence

2025/04/30 by Sun, Yuze
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2504.21483

Abstract

A morphism from a diagonalizable group G to the torus of a toric variety X induces an action of G on X. We prove the category of ind-coherent sheaves on the quotient stack is equivalent to the category of sheaves on a cover of a real torus with singular supports contained in the FLTZ skeleton, extending Kuwagaki's nonequivariant coherent-constructible correspondence arXiv:1610.03214. We also investigate the functoriality of such correspondence for toric morphisms and inclusions of orbit closures.

Citations

• The reductive Borel-Serre compactification as a model for unstable algebraic K-theory
• Mirror symmetry for very affine hypersurfaces
• Sheaves of categories and the notion of 1-affineness
• Toric Stacks I: The Theory of Stacky Fans
• Toric Stacks II: Intrinsic Characterization of Toric Stacks
• A categorification of Morelli's theorem
• Remarks on the nonequivariant coherent-constructible correspondence for toric varieties
• The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks
• Derived Categories of Toric Varieties

Related

• Coherent-Constructible Correspondence for Toric Fibrations
• Remarks on the nonequivariant coherent-constructible correspondence for toric varieties
• The nonequivariant coherent-constructible correspondence and tilting
• Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric Varieties
• The nonequivariant coherent-constructible correspondence for toric surfaces