Containment problem for points on a reducible conic in $\mathbb{P}^2$

Annika Denkert; Mike Janssen

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arXiv · 1207.7153

Containment problem for points on a reducible conic in $\mathbb{P}^2$

Annika Denkert·Mike Janssen

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Abstract

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.

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Annika Denkert, Mike Janssen. 2013-05-15. Containment problem for points on a reducible conic in $\mathbb{P}^2$. https://arxiv.org/abs/1207.7153

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