Polarized interpolation and normal postulation for curves on Fano hypersurfaces

2023/08/04 by Ziv Ran, Ran, Ziv
Mathematics · Medicine · Social Sciences · #14j45 #14m22 #14n25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Spinal Hematomas and Complications #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2308.02089

openalex publication_date 2023/08/04 · openalex created_date 2023/08/08 · openalex updated_date 2026/07/28

Abstract

A general hypersurface X of degree ≤ n in projective space contains curves C of any genus g≥ 0 and sufficiently large degree depnding on g whose normal and conormal bundles have good postulation or natural cohomology in the sense that each twist has either H⁰=0 or H¹=0. This implies a polarized version of the interpolation property for C on X.

Related

• Interpolation of curves on Fano hypersurfaces
• Curves with stable or semistable normal bundle on Fano hypersurfaces
• Interpolation for normal bundles of general curves
• Families of canonically polarized varieties over surfaces
• Polarized minimal families of rational curves and higher Fano manifolds