Toric varieties with NC toric actions: NC type IIA geometry

NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration

Using the algebraic geometry method of Berenstein and Leigh ( BL ), hepth/0009209 and hep-th/0105229 ), and considering singular toric varieties Vd+1 with NC irrational torus fibration, we construct NC extensions M (nc) d of complex d dimension Calabi-Yau (CY) manifolds embedded in V (nc) d+1 . We give realizations of the NC C toric group, derive the constraint eqs for NC CalabiYau ( NCCY ) man...

The Geometry of Toric Varieties

Toric 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...

Secant 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...

Homogeneous 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 ...