Counterexamples to containment problems for fat points schemes in the projective plane via multiplier ideals

2017/02/24 by Víctor González‐Alonso, González-Alonso, Víctor, Piotr Pokora +1
Computer Science · Mathematics · #13A15 #13F20 #14C20 #14F18 #14J26 #14N20 #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1702.07509

openalex publication_date 2017/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we address the relation between symbolic and ordinary powers of the ideal of a reduced set or points in projective space: the so-called containment problem. In particular, we obtain sharp lower bounds on the Waldschmidt constants of ideals of points in the plane not satisfying I^(2r-1) ⊆ I^r.

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