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arXiv · 2602.16945

On rational chain connectedness of globally +-regular varieties

Emre Alp Özavcı·Zsolt Patakfalvi·Kevin Tucker·Joe Waldron·Zheng Xu
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Abstract

We prove that globally $+$-regular varieties are rationally chain connected in dimension three and mixed characteristic with residue field characteristic $p>5$. We also introduce a notion of strongly globally $+$-regular, and show that varieties of arbitrary dimension which are strongly globally $+$-regular over a dense open subset of $\mathrm{Spec}(\mathbb{Z})$ are rationally chain connected.

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Emre Alp Özavcı, Zsolt Patakfalvi, Kevin Tucker, Joe Waldron, Zheng Xu. 2026-02-18. On rational chain connectedness of globally +-regular varieties. https://arxiv.org/abs/2602.16945

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