منابع مشابه
Cartier Isomorphism for Toric Varieties
is an isomorphism. Here F : X −→ X denotes the Frobenius morphism on X and H denotes the a cohomology sheaf of F∗Ω•X . If the variety is not smooth, not much is known about the properties of the Cartier operator and the poor behaviour of the deRham complex in this case makes its study difficult. If one substitutes the deRham complex with the Zariski-deRham complex the situation is better. For e...
متن کاملToric Varieties
4.1.5. The weighted projective space P(q0, . . . ,qn), gcd(q0, . . . ,qn) = 1, is built from a fan in N = Z/Z(q0, . . . ,qn). Let ui ∈ N be the image of ei ∈ Z . The dual lattice is M = {(a0, . . . ,an) ∈ Z n+1 | a0q0+ · · ·+anqn = 0}. Also assume that gcd(q0, . . . , q̂i, . . . ,qn) = 1 for i = 0, . . . ,n. (a) Prove that the ui are the primitive ray generators of the fan giving P(q0, . . . ,qn...
متن کاملSecant Varieties of Toric Varieties
If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...
متن کاملKoszul Duality for Toric Varieties
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.
متن کاملHomogeneous Toric Varieties
A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The result is based on the Cox realization of a toric variety as a quotient space of an open subset of a vector space V by a quasitorus action and on investigation ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8569