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 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 Poincaré polynomials for a large class of singular toric varieties.

Torus orbit closures in the flag variety

“…We refer the reader to [7] for a precise definition of retraction sequences. It is shown in [57] that a linear function h in Lemma 4.15 defines a retraction sequence on the polytope Q w . However, it is not known whether all retraction sequences come from linear functions.…”