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arXiv · 2405.14330

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

Valery A. Lunts
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Abstract

Let X be a smooth toric variety defined by the fan {\Sigma} . We consider {\Sigma} as a finite set with topology and define a natural sheaf of graded algebras A_{\Sigma} on {\Sigma} . The category of modules over A_{\Sigma} 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_{\Sigma} . Eventually (for a complete X ) the combinatorial Koszul duality is interpreted in terms of the Serre functor on D^b(coh_{X,T})

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Valery A. Lunts. 2024-05-23. Derived category of equivariant coherent sheaves on a smooth toric variety and Koszul duality. https://arxiv.org/abs/2405.14330

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