# Conic decomposition of a toric variety and its application to cohomology

@inproceedings{Park2021ConicDO, title={Conic decomposition of a toric variety and its application to cohomology}, author={Seonjeong Park and Jongbaek Song}, year={2021} }

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.

## 2 Citations

### Torus orbit closures in the flag variety

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- 2022

. The study of torus orbit closures in the (complete) ﬂag variety was initiated by Klyachko and Gelfand–Serganova in the mid-1980s, but it seems that not much has been done since then. In this…

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