A proof of the Briancon-Iarrobino Conjecture in three dimensions
Abstract
We resolve the 1978 Briancon-Iarrobino Conjecture regarding the maximum singularity of H=Hilbl(A3), where l is a tetrahedral number, by refining the work of Ramkumar-Sammartano in Ramkumar-Sammartano. This also immediately implies the conjectural necessary condition for a point of H to have the maximal singularity, suggested by the second-named author in Rezaee-23-Conjectures. In a sequel to this article, Mackenzie-Rezaee2, we prove a generalized version of this conjecture for certain non-tetrahedral l, via proving the conjectural necessary condition.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.