Containment results for ideals of various configurations of points in [formula omitted

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 PN. 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.