We introduce the notion of a \emph{ 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 with certain regulations. 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 Poincar\'e polynomials for a large class of singular toric varieties.
Categories: math.AT math.AG math.CO