Fat lines in P³: powers versus symbolic powers

2012/08/26 by Elena Guardo, Guardo, Elena, Brian Harbourne +3 · 1 citation
Computer Science · Mathematics · #13A15 #13F20 #14C20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1208.5221

openalex publication_date 2012/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the symbolic and regular powers of ideals I for a family of special configurations of lines in P³. For this family, we show that I^(m) = I^m for all integers m if and only if I^(3) = I³. We use these configurations to answer a question of Huneke that asks whether I^(m) = I^m for all m if equality holds when m equals the big height of the ideal I.

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