Year: 2025
Type: preprint
Abstract: In this paper, we establish a real closed analogue of Bertini's theorem. Let $R$ be a real closed field and $X$ a formally real integral algebraic variety over $R$. We show that if the zero locus of a nonzero global section $s$ of an invertible sheaf on $X$ has a formally real generic point, then $s$ does not change sign on $X$, and vice versa under certain conditions. As a consequence, we demonstrate that there exists a nonempty open subset of hypersurface sections preserving formal reality and integrality for quasi-projective varieties of dimension $\geq 2$ under these conditions.
Source: arXiv (Cornell University)
Authors: Ouyang, Yi, Zhang, Chenhao
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3857364911, G4313471612
OpenAlex ID: W4416019553
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