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arXiv · 2502.05681

$p$-anisotropy on the moment curve for homology manifolds and cycles

Karim Adiprasito·Kaiying Hou·Daishi Kiyohara·Daniel Koizumi·Monroe Stephenson
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Abstract

We prove that the Gorensteinification of the face ring of a cycle is totally $p$-anisotropic in characteristic $p$. In other words, given an appropriate Artinian reduction, it contains no nonzero $p$-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically.

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Karim Adiprasito, Kaiying Hou, Daishi Kiyohara, Daniel Koizumi, Monroe Stephenson. 2025-11-10. $p$-anisotropy on the moment curve for homology manifolds and cycles. https://arxiv.org/abs/2502.05681

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