Containment counterexamples for ideals of various configurations of points in PN

By Brian Harbourne, Alexandra Seceleanu. 2013

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Abstract When I is the radical homogeneous ideal of a finite set of points in projective N-space, P N , over a field K, it has been conjectured that I ( r N − N + 1 ) should be contained in I r for all r ≥ 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 .

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d8d1eaac35e616b0b1e5f263c1cf9199807368c5