On the containment problem for fat points ideals

Abstract

In this note we show that Harbourne's conjecture is true for symbolic powers of ideals of points, we check that the stable version of this conjecture is valid for ideals of very general points (resp. generic points) in ${\mathbb{P}}_{\mathbb{K}}^N$ (resp. ${\mathbb{P}}_{\mathbb{K}(\underline{z})}^N$). We also show that this conjecture and the Harbourne-Huneke conjecture are true for a class of ideals $I$ defining fat points obtained from line arrangements in ${\mathbb{P}}_{\mathbb{K}}^2$.

7 pages

References in corpus (2)

• On the containment problem
• A stable version of Harbourne's Conjecture and the containment problem for space monomial curves