Conic decomposition of a toric variety and its application to cohomology

Abstract

We introduce the notion of a conic sequence of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one according to certain rules. We apply this to a toric variety to obtain an iterated cofibration structure on it. This allows us to prove several vanishing results in the rational cohomology of a toric variety and to calculate the Poincaré polynomials for a large class of singular toric varieties.