2022/11/23 by Ziv Ran, Ran, Ziv
Mathematics · #14j45 #14m22 #14n25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2211.12661
openalex publication_date 2022/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For every n≥ 3, g≥ 1 and all large enough e depending on n,g, there exist curves of genus g, degree e in a general hypersurface of degree n in \mathbb Pn, or in \mathbb Pn itself, whose whose normal bundle N is stable, as is any sufficiently general full-rank subsheaf of N. For g=1, N is semi-stable. On general hypersurface of degree d< n in \mathbb Pn, such that a certain arithmetical condition on d,n, g holds, there exists an arithmetical progression of e values so that curves of degree e and genus g with semistable normal bundle exist. Previous results were restricted to certain cases with ambient space ¶n