Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Singularities in Positive and Mixed Characteristic Commutative Algebra, G2381409970, Collaborative Research: Bridging Singularities in Algebra and Geometry Across Characteristics, Birational classification of varieties: connections to arithmetic and algebra, CAREER: New Frontiers in Birational Geometry - Novel Arithmetic Techniques and Applications, G993971353
OpenAlex ID: W7130732018