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

Abstract

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 contained in $I^r$ for all $r\ge 1$. Recent counterexamples show that this can fail when N=r=2. We study properties of the resulting ideals. We also show that failures occur for infinitely many $r$ in every characteristic $p>2$ when N=2, and we find additional positive characteristic failures when $N>2$.

11 pages

References in corpus (4)

• Are symbolic powers highly evolved?
• Containment results for ideals of various configurations of points in P^N
• Containment problem for points on a reducible conic in ${\mathbb{P}}^2$
• Symbolic powers of ideals of generic points in P^3

Cited by in corpus (2)

• Resurgences for ideals of special point configurations in ${\mathbf{P}}^N$ coming from hyperplane arrangements
• The Alpha Problem & Line Count Configurations