Containment results for ideals of various configurations of points in P^N

Abstract

Guided by evidence coming from a few key examples and attempting to unify previous work of Chudnovsky, Esnault-Viehweg, Eisenbud-Mazur, Ein-Lazarsfeld-Smith, Hochster-Huneke and Bocci-Harbourne, Harbourne and Huneke recently formulated a series of conjectures that relate symbolic and regular powers of ideals of fat points in ${\mathbf{P}}^N$. In this paper we propose another conjecture along the same lines (Conjecture 3.9), and we verify it and the conjectures of Harbourne and Huneke for a variety of configurations of points.

Version 3 adds Remark 3.11, regarding recent counterexamples, 14 pages (version 2 added new conjecture, Conjecture 3.9, and fixed typos with slight change to abstract)

References in corpus (1)

• Symbolic powers of ideals of generic points in P^3

Cited by in corpus (6)

• Resurgences for ideals of special point configurations in ${\mathbf{P}}^N$ coming from hyperplane arrangements
• On a class of power ideals
• Containment Counterexamples for ideals of various configurations of points in ${\mathbf{P}}^N$
• The Alpha Problem & Line Count Configurations
• Symbolic powers versus regular powers of ideals of general points in P^1 x P^1
• Fat lines in P^3: powers versus symbolic powers