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

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 $I^{(2r-1)}\subseteq I^r$.

There is a gap in our proof of the main theorem which is, at this stage, not fixable

References in corpus (2)

• On the containment problem
• On a conjecture of Demailly and new bounds on Waldschmidt constants in ${\mathbb{P}}^N$