A homological criterion for the containment between symbolic and ordinary powers for some ideals of points in ℙ²

2014/10/01 by Alexandra Seceleanu, Seceleanu, Alexandra
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Topological and Geometric Data Analysis #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1410.0312

Abstract

We establish a criterion for the (failure of) the containment I^(m)⊂ I^r for 3-generated ideals I defining reduced sets of points in ℙ². Our criterion arises from studying the minimal free resolutions of the powers of I, specifically the minimal free resolutions for I^m and I^r. We apply this criterion to two point configurations that have recently arisen as counterexamples to a question of B. Harbourne and C. Huneke: the Fermat configuration and the Klein configuration.

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