2007/10/08 by Edoardo Ballico, Ballico, Edoardo, Monica Idà +1
Computer Science · Mathematics · #14N05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:14N05
paper · pdf · doi:10.48550/arxiv.0710.1588
18 pages
arxiv created 2007/10/08 · openalex publication_date 2007/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Z be a fat point scheme in P2 supported on general points. Here we prove that if the multiplicities are at most 3 and the length of Z is sufficiently high then the number of generators of the homogeneous ideal IZ in each degree is as small as numerically possible. Since it is known that Z has maximal Hilbert function, this implies that Z has the expected minimal free resolution.