Displaying the cohomology of toric line bundles

Cohomology of toric bundles

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

5 Cohomology of toric bundles

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

The Orbifold Cohomology Ring of Simplicial Toric Stack Bundles

We compute the orbifold cohomology ring of the simplicial toric stack bundles. We give an example to show that the ordinary cohomology ring of the crepant resolution of a simplicial toric stack bundle is not necessarily isomorphic to its orbifold cohomology ring.

Structure of Cohomology of Line Bundles on G/B for Semisimple Groups Short running title: Cohomology of Line Bundles

Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field k of characteristic p > 0, T a maximal torus of G and B a Borel subgroup containing T . Each weight in X(T ) determines a line bundle on the flag varietyG/B. It turns out that cohomology of the line bundle is isomorphic to the derived functor of the induction functors from the category of B-m...

Principal Parts of Line Bundles on Toric Varieties