2020/08/03 by Ziv Ran, Ran, Ziv
Mathematics · #14j45 #14m22 #14n25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2008.01235
openalex publication_date 2020/08/03 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28
On a general Fano hypersurface in projective space, we determine for infinitely many k the minimal degree e of a rational curve through a general collection of k points. In the case of a hypersurface of index 1, our results hold for all k≥ 1. In an appendix, M.C. Chang proves an arithmetical result which implies that in the case of index >1, the density of the set of curve degrees e covered by our method is approximately ((n-d)(d-(5)/(2)))/((n-2)d).