Containment Counterexamples for ideals of various configurations of points in ${\mathbf{P}}^N$

Brian Harbourne, Alexandra Seceleanu

When $I$ is the radical homogeneous ideal of a finite set of points in projective $N$-space, ${\mathbf{P}}^N$, over a field $K$, it has been conjectured that $I^{(rN-N+1)}$ should be co…