An interpolation problem for the normal bundle of curves of genus g≥ 2 and high degree in \mathbb P^r

2014/04/24 by Edoardo Ballico, E. Ballico, Ballico, E.
Engineering · Mathematics · #14H50 #14H60 #Advanced Algebra and Geometry #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14H50 #msc:14H60

paper · pdf · doi:10.48550/arxiv.1404.6056

arxiv created 2014/04/24 · openalex publication_date 2014/04/24 · arxiv updated 2014/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C⊂ \mathbb Pⁿ be a smooth curve and N_C its normal bundle. N_C satisfies strong interpolation if for all integers s>0 and λ_i∈ \0,1,… ,n-1\, 1≤ i ≤ s, there are distinct points P₁,… ,P_s∈ C and linear subspaces U_i⊆ E|P_i such that dim (U_i)= λ_i for all i and the evaluation map H⁰(E)→ ⊕ _i=1^s U_i has maximal rank (A. Atanasios). We prove that C satisfies strong interpolation if either C is a linearly normal elliptic curve or C is a general embedding of degree d≥ (5n-8)g+2n²-5n+4 of a smooth curve X of genus g≥ 2.

Related

• Interpolation for normal bundles of general curves
• Interpolation and vector bundles on curves
• Interpolation for Curves in Projective Space with Bounded Error
• Interpolation of Varieties of Minimal Degree
• Interpolation in Algebraic Geometry