Koszul Duality for Toric Varieties
نویسنده
چکیده
We show that certain categories of perverse sheaves on affine toric varieties Xσ and Xσ∨ defined by dual cones are Koszul dual in the sense of Beilinson, Ginzburg and Soergel [BGS]. The functor expressing this duality is constructed explicitly by using a combinatorial model for mixed sheaves on toric varieties.
منابع مشابه
Weights in the cohomology of toric varieties
We describe the weight filtration in the cohomology of toric varieties. We present the role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We also obtain a results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complex IH∗ T (X)⊗ H ∗(T ).
متن کاملFrobenius Splittings of Toric Varieties
We discuss a characteristic free version of Frobenius splittings for toric varieties and give a polyhedral criterion for a toric variety to be diagonally split. We apply this criterion to show that section rings of nef line bundles on diagonally split toric varieties are normally presented and Koszul, and that Schubert varieties are not diagonally split in general.
متن کاملMultigraded regularity and the Koszul property
We give a criterion for the section ring of an ample line bundle to be Koszul in terms of multigraded regularity. We discuss applications to adjoint bundles on toric varieties as well as to polytopal semigroup rings.
متن کاملLattice polytopes cut out by root systems and the Koszul property
We show that lattice polytopes cut out by root systems of classical type are normal and Koszul, generalizing a well-known result of Bruns, Gubeladze, and Trung in type A. We prove similar results for Cayley sums of collections of polytopes whose Minkowski sums are cut out by root systems. The proofs are based on a combinatorial characterization of diagonally split toric varieties.
متن کاملOn Torsion in Homology of Singular Toric Varieties
Let X be a toric variety. Rationally Borel-Moore homology of X is isomorphic to the homology of the Koszul complex A ∗ (X)⊗Λ∗M , where A T ∗ (X) is the equivariant Chow group and M is the character group of T . Moreover, the same holds for coefficients which are the integers with certain primes inverted.
متن کامل