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Bier spheres and toric topology

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arxiv 2406.03597 v2 pith:MKS5DMAA submitted 2024-06-05 math.AT math.CO

Ivan Limonchenko , Matvey Sergeev This is my paper · ORCID
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keywords biercomplexcomputecorrespondingnervespherestoricapplication
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We compute the real and complex Buchstaber numbers of an arbitrary Bier sphere. In dimension two, we identify all the 13 different combinatorial types of Bier spheres and show that 12 of them are nerve complexes of nestohedra, while the remaining one is a nerve complex of a generalized permutohedron. As an application of our results, we construct a regular normal fan for each of those 13 Delzant polytopes, compute the cohomology rings of the corresponding nonsingular projective toric varieties, and examine the orientability of the corresponding small covers.

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Cited by 1 Pith paper

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  1. Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture

    math.CO 2024-11 conditional novelty 7.0 of 10

    Flag Murai spheres are exactly the nerve complexes of four families of flag nestohedra, which implies the Nevo-Petersen conjecture for them.

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