2009/11/29 by Mihai Halic, Halic, Mihai · 1 citation
Mathematics · #14D15 #14H10 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14D15 #msc:14H10 #msc:14J28
paper · pdf · doi:10.48550/arxiv.0911.5474
arxiv created 2009/11/29 · openalex publication_date 2009/11/29 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we partially address two issues: - The first is a rigidity property for pairs (S,C) consisting of a general projective K3 surface S, and a curve C obtained as the normalization of a nodal, hyperplane section of S. We prove that a non-trivial deformation of such a pair (S,C) induces a non-trivial deformation of C; - The second question concerns the Wahl map of curves C as above. We prove that the Wahl map of the normalization of a nodal curve contained in a general projective K3 surface is non-surjective. In both cases, we impose upper bounds on the number of nodes of the hyperplane section.