Hilbert functions and resolutions for ideals of n = s² fat points in P2

2001/04/26 by Brian Harbourne, Harbourne, Brian, Joaquím Roé +2
Computer Science · Mathematics · #13P10 #14C99 #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:13P10 #msc:14C99

paper · pdf · doi:10.48550/arxiv.math/0104254

10 pages, 4 color postscript graphics

arxiv created 2001/04/26 · openalex publication_date 2001/04/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Conjectures for the Hilbert function of the m-th symbolic power of the ideal of n general points of P2 are verified for infinitely many m for each square n > 9, using an approach developed by the authors in a previous paper. In those cases that n is even, conjectures for the resolution are also verified. Previously, by work of Evain (for the Hilbert function) and of Harbourne, Holay and Fitchett (for the resolution), these conjectures were known for infinitely many m for a given n > 9 only for n being a power of 4.

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