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arXiv · 2106.04429

Conic decomposition of a toric variety and its application to cohomology

Seonjeong Park·Jongbaek Song
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Abstract

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.

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Seonjeong Park, Jongbaek Song. 2021-06-08. Conic decomposition of a toric variety and its application to cohomology. https://arxiv.org/abs/2106.04429

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