2001/01/12 by Stephanie Fitchett, Fitchett, Stephanie, Brian Harbourne +3
Computer Science · Mathematics · #13P10 #14C99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG #msc:13P10 #msc:14C99
paper · pdf · doi:10.48550/arxiv.math/0101110
12 pages PlainTeX
arxiv created 2001/01/12 · openalex publication_date 2001/01/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result provides an algorithm for determining the minimal free resolution of ideals of fat point subschemes of \bf P2 involving up to 8 general points with arbitrary multiplicities; the results hold over algebraically closed fields of any characteristic. The algorithm, which works by giving a formula in certain cases and a reduction to these cases otherwise, does not involve Gröbner bases, and so is very fast, even for very large multiplicities. Partial information is also obtained in certain cases with n>8.