1999/06/18 by Brian Harbourne, Harbourne, Brian, Sandeep Holay +3
Computer Science · Mathematics · #13P10 #14C99 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #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/9906130
arxiv created 1999/06/18 · openalex publication_date 1999/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let I be the ideal corresponding to a set of general points p1,...,pn ∈ P2. There recently has been progress in showing that a naive lower bound for the Hilbert functions of symbolic powers I(m) is in fact attained when n>9. Here, for m sufficiently large, the minimal free graded resolution of I(m) is determined when n>9 is an even square, assuming only that this lower bound on the Hilbert function is attained. Under ostensibly stronger conditions (that are nonetheless expected always to hold), a similar result is shown to hold for odd squares, and for infinitely many m for each nonsquare n bigger than 9. All results hold for an arbitrary algebraically closed field k.