2023/09/21 by Qixiao Ma, Ma, Qixiao · 1 citation
Mathematics · #14G05 #14G27 #14J70 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2309.12208
openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Over fields of characteristic zero, we show that for n=1,d≥4 or n=2,d≥5 or n≥3, d≥ 2n, the generic m-marked degree-d hypersurface in ℙn+1 admits the m marked points as all the rational points. Over arbitrary fields, we show that for n=1,d≥4 or n≥2, d≥ 2n+3, the identiy map is the only rational self-map of the generic degree-d hypersurface in ℙn+1.