Unirationality of hypersurfaces via highly tangent lines

2025/11/10 by Cheng, Raymond
#14M10 (secondary) #14M20 (primary) 14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.07545

Abstract

This article describes a unirationality construction for general low degree complete intersections in projective space which is based on a variety of highly tangent lines. Applied to hypersurfaces, this implies that a general hypersurface of degree d ≥ 6 in projective n-space is unirational as soon as n ≥ 2^(d-1)2^d-5, significantly improving classical bounds.

Citations

• Profiles, linear spaces, and unirationality of complete intersections
• On a Conjecture on the Variety of Lines on a Fano Complete Intersection
• Tropical degenerations and stable rationality
• Linear subspaces of hypersurfaces

Related

• Lines highly tangent to a hypersurface
• Unirationality of varieties described by families of projective hypersurfaces
• A transfer principle for unirationality
• Unirationality and geometric unirationality for hypersurfaces in positive characteristics
• Nondeformability of entire curves in projective hypersurfaces of high degree