3-fold symmetric products of curves as hyperbolic hypersurfaces in \Proj⁴

2003/01/09 by Ciro Ciliberto, Mikhail Zaidenberg, Ciliberto, Ciro +1
Mathematics · #14J70 (Primary) 32Q45 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AG #msc:14J70 #msc:32Q45

paper · pdf · doi:10.48550/arxiv.math/0301082

22 pages, LaTeX

arxiv created 2003/01/09 · openalex publication_date 2003/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct new examples of Kobayashi hyperbolic hypersurfaces in the projective 4-space. They are generic projections of the triple symmetric product of a generic curve of genus at least 7, smoothly embedded in the projective 7-space.

Citations

• Beyond a conjecture of Clemens

Related

• Hyperbolic surfaces in \bf P³: examples
• Hyperbolicity and Specialness of Symmetric Powers
• On the hyperbolicity of general hypersurfaces
• Hyperbolicity of general deformations
• Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces