Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Fan cohomology and equivariant Chow rings of toric varieties
Toric varieties are varieties equipped with a torus action and constructed from cones and fans. In the joint work with Suanne Au and Mark E. Walker, we prove that the equivariant K-theory of an affine toric variety constructed from a cone can be identified with a group ring determined by the cone. When a toric variety X(Δ) is smooth, we interpret equivariant K-groups as presheaves on the associated fan space Δ. Relating the sheaf cohomology groups to equivariant K-groups via a spectral sequence, we provide another proof of a theorem of Vezzosi and Vistoli: equivariant K-theory is formed by patching equivariant K-theory of equivariant affine toric subvarieties. ^ This dissertation studies the sheaf cohomology groups for the equivariant K-groups tensored with Q and completed, and how they relate to the equivariant K-groups of non-smooth and non-affine toric varieties. The equivariant K-groups tensored with Q and completed coincide with the equivariant Chow rings for affine toric varieties. For a three-dimensional complete fan, we calculate the dimensions of the sheaf cohomology groups for the symmetric algebra sheaf. When the fan is given by a convex polytope, this information computes the equivariant K-groups tensored with Q and completed as extensions of sheaf cohomology groups.^
Huang, Mu-wan, "Fan cohomology and equivariant Chow rings of toric varieties" (2009). ETD collection for University of Nebraska - Lincoln. AAI3360497.