2003/04/09 by Joaquím Roé, Joaquim Roé, Roé, Joaquim
Computer Science · Mathematics · #14C20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C20
paper · pdf · doi:10.48550/arxiv.math/0304124
8 pages
arxiv created 2003/04/09 · openalex publication_date 2003/04/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
T. Szemberg proposed in 2001 a generalization to arbitrary varieties of M. Nagata's 1959 open conjecture, which claims that the Seshadri constant of r>9 very general points of the projective plane is maximal. Here we prove that Nagata's original conjecture implies Szemberg's for all smooth surfaces X with an ample divisor L generating its Neron-Severi group and such that L2 is a square. More generally, we prove that the (n-1)-dimensional Seshadri constant of an ample divisor L on a projective variety X of dimension n at r very general points is bounded below by the product of the (n-1)-dimensional Seshadri constant of at a very general point times the (n-1)-dimensional Seshadri constant of the hyperplane on projective n-space at r very general points.