Containment problem for points on a reducible conic in $\mathbb{P}^2$
  Given an ideal $I$ in a Noetherian ring, one can ask the containment question: for which $m$ and $r$ is the symbolic power $I^{(m)}$ contained in the ordinary power $I^r$? C. Bocci and B. Harbourne study the containment question in a geometric setting, where the ideal $I$ is in a polynomial ring over a field. Like them, we will consider special geometric constructs. In particular, we obtain a complete solution in two extreme cases of ideals of points on a pair of lines in $\mathbb{P}^2$; in one case, the number of points on each line is the same, while in the other all the points but one are on one of the lines. 
Annika Denkert and Mike Janssen
math.AG math.AC