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

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

2011-09-09

arxiv.org/abs/1109.1884v2

Mathematics

Algebraic Geometry

15 pages; added new conjecture (Conjecture 3.9) and fixed typos; slight change to abstract

Scientific paper

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.

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