2020/08/04 by Serge Lvovski, Lvovski, Serge
Mathematics · #14H50 (Primary) #14N99 #53D10 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2008.01418
openalex publication_date 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if a smooth projective curve C⊂\mathbb P3 (over an algebraically closed field of characteristic zero) is Legendrian with respect to a contact structure (it is well known that a contact structure on \mathbb P3 is unique up to a linear automorphism) and C is linearly normal (i.e., not an isomorphic linear projection of a smooth curve C'⊂\mathbb Pn, n>3, where C' does not lie in a hyperplane) then C is a twisted cubic or a line.