Containment problem for points on a reducible conic in ℙ²

2012/07/31 by Denkert, Annika, Janssen, Mike
#13F20 #14C20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.7153

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 ℙ²; 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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