2013/12/19 by Marcin Dumnicki, Dumnicki, Marcin, Brian Harbourne +8
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.1312.5549
25 pages, 2 figures. Updated version of the Oberwolfach Preprint OWP 2013-22, with some new material. Comments welcome
openalex publication_date 2013/12/19 · arxiv created 2016/02/05 · arxiv updated 2016/02/08 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
It is well known that multi-point Seshadri constants for a small number s of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their values are maximal for s≥ 9 points. Tackling the problem in the language of valuations one can make sense of s points for any positive real s≥ 1. We show somewhat surprisingly that a Nagata-type conjecture should be valid for s≥ 8+1/36 points and we compute explicitly all Seshadri constants (expressed here as the asymptotic maximal vanishing element) for s≤ 7+1/9.