1999/09/16 by Brian Harbourne, Harbourne, Brian
Computer Science · Mathematics · #14N99 #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory #math.AG #msc:14N99
paper · pdf · doi:10.48550/arxiv.math/9909093
6 pages
arxiv created 1999/09/16 · openalex publication_date 1999/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modifying an approach of J. Roe, this paper gives an improved lower bound on the degrees d such that for general points p1,...,pn in P2 and m > 0 there is a plane curve of degree d vanishing at each point pi with multiplicity at least m. In certain cases, for m not too large compared with n, the new bound implies a bound conjectured by Nagata.