Singular loci of reflection arrangements and the containment problem

Chudnovsky’s conjecture and the stable Harbourne–Huneke containment

“…In fact, several of the counterexamples to Harbourne's Conjecture that appear in the literature, such as the Fermat [DSTG13, HS15], Klein and Wiman configurations [Kle78, Wim96, Sec15], turn out to arise in this form. Drabkin and Seceleanu studied this class of ideals [DS20], and in particular completely classified which I among these satisfy the containment I (3) ⊆ I 2 . Fix such an ideal I, which has pure height 2, and assume that G is an irreducible reflection group of rank three.…”

“…The authors thank Grzegorz Malara and Halszka Tutaj-Gasińska for their suggestion to look at Böröczky configurations, and Alexandra Seceleanu for pointing to [DHN + 15], all of which resulted in Example 3.8. We also thank Alexandra Seceleanu for kindly sharing the new version of [DS20], which led to Example 3.9. We also thank Jack Jeffries for helpful discussions, and Justyna Szpond and Tomasz Szemberg for comments on an early draft of this paper.…”