Rational curves of degree 16 on a general heptic fourfold

2012/06/13 by Ethan Cotterill, Cotterill, Ethan
Computer Science · Mathematics · #14N10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14N10

paper · pdf · doi:10.48550/arxiv.1206.2811

13 pages

arxiv created 2012/06/13 · openalex publication_date 2012/06/13 · arxiv updated 2012/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

According to a conjecture of H. Clemens, the dimension of the space of rational curves on a general projective hypersurface should equal the number predicted by a naïve dimension count. In the case of a general hypersurface of degree 7 in ℙ⁵, the conjecture predicts that the only rational curves should be lines. This has been verified by Hana and Johnsen for rational curves of degree at most 15. Here we extend their results to show that no rational curves of degree 16 lie on a general heptic fourfold.

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