Conic decomposition of a toric variety and its application to cohomology

Park, Seonjeong; Song, Jongbaek

doi:10.1090/proc/15876

Conic decomposition of a toric variety and its application to cohomology
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by Seonjeong Park and Jongbaek Song PDF

Proc. Amer. Math. Soc. 150 (2022), 2777-2792 Request permission

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.

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