%0 Journal Article
%T A homological criterion for the containment between symbolic and ordinary powers for some ideals of points in $\mathbb{P}^2$
%A Alexandra Seceleanu
%J Mathematics
%D 2014
%I arXiv
%X We establish a criterion for the (failure of) the containment $I^{(m)}\subset I^r$ for 3-generated ideals $I$ defining reduced sets of points in $\mathbb{P}^2$. Our criterion arises from studying the minimal free resolutions of the powers of $I$, specifically the minimal free resolutions for $I^m$ and $I^r$. We apply this criterion to two point configurations that have recently arisen as counterexamples to a question of B. Harbourne and C. Huneke: the Fermat configuration and the Klein configuration.
%U http://arxiv.org/abs/1410.0312v2