Derived category of equivariant coherent sheaves on a smooth toric variety and Koszul duality

2024/05/23 by Valery A. Lunts, Lunts, Valery A.
Mathematics · #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2405.14330

Abstract

Let X be a smooth toric variety defined by the fan Σ . We consider Σ as a finite set with topology and define a natural sheaf of graded algebras A_Σ on Σ . The category of modules over A_Σ is studied (together with other related categories). This leads to a certain combinatorial Koszul duality equivalence. We describe the equivariant category of coherent sheaves coh_X,T and a related (slightly bigger) equivariant category O_X,T-mod in terms of sheaves of modules over the sheaf of algebras A_Σ . Eventually (for a complete X ) the combinatorial Koszul duality is interpreted in terms of the Serre functor on D^b(coh_X,T)

Related

• Koszul duality for toric varieties
• Equivariant-constructible Koszul duality for dual toric varieties
• Koszul Algebras and Sheaves over Projective Space
• Categorical cyclic homology and filtered D-modules on stacks: Koszul duality
• A category of kernels for equivariant factorizations, II: further\n implications