Containment results for ideals of various configurations of points in

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 . 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.