Containment results for ideals of various configurations of points in P^N
arXiv:1109.1884
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 ${\bf P}^N$. 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)