2025/12/17 by Beheshti, Roya, Mukhopadhyay, Shibashis, Riedl, Eric
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2512.15903
openalex publication_date 2025/12/17 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28
Let X be a smooth hypersurface of degree d in Pn over an algebraically closed field of characteristic p. We show that X must be separably rationally connected and must contain a free line if either p is at least d or if p is at least d-1 and the defining equation has some partial derivative that is not too singular. We also show that X must be separably rationally connected in any characteristic if d = 4 and n is sufficiently large. Along the way, we generalize results on the spaces of k-planes in X to characteristic p and connect some of these questions to the spaces of linear sections of X.