2025/11/05 by Yi Ouyang, Chenhao Zhang, Ouyang, Yi +1
Computer Science · Mathematics · #12J15 #14P25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2511.03277
openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28
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 ≥ 2 under these conditions.