Rational curves on hypersurfaces of low degree, II

2002/07/27 by Joe Harris, Jason Starr, Harris, Joe +1
Computer Science · Engineering · Mathematics · #14C05 #14N25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C05 #msc:14N25

paper · pdf · doi:10.48550/arxiv.math/0207257

47 pages

arxiv created 2002/07/27 · openalex publication_date 2002/07/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a continuation of "Rational curves on hypersurfaces of low degree", math.AG/0203088. We prove that if d²+d+1 < n and d > 2, then for a general hypersurface X_d in Pⁿ of degree d, for each degree e the space of rational curves of degree e on X is itself a rationally connected variety.

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