Abstract:

If a complex algebraic torus T=(C^*)^n acts on a complex projective algebraic variety X, then the equivariant cohomology H^*_T(X) is a module over the equivariant cohomology of a point. Under fairly mild hypotheses, the equivariant cohomology of X can be interpreted as the set of functions on a certain affine variety, denoted Spec(H^*_T(X)). This variety often turns out to be an arrangement of linear subspaces of C^n. Arrangements of this type can be studied by combinatorial techniques, and this sometimes leads to combinatorial formulas for the cohomology of X.