Chudnovsky's Conjecture and the stable Harbourne-Huneke containment for general points

Abstract

In our previous work with Grifo and Hà, we showed the stable Harbourne-Huneke containment and Chudnovsky's conjecture for the defining ideal of sufficiently many general points in ${\mathbb{P}}^N$. In this paper, we establish the conjectures for all remaining cases, and hence, give the affirmative answer to Harbourne-Huneke containment and Chudnovsky's conjecture for any number of general points in ${\mathbb{P}}^N$ for all $N$. Our new technique is to develop the Cremona reduction process that provides effective lower bounds for the Waldschmidt constant of the defining ideals of generic points in projective spaces.

arXiv commentComments are welcome. New version: Harbourne-Huneke stable containment and Chudnovsky's conjecture are proved for any number of general points