Year: 2026
Type: preprint
Abstract: We show the existence of a quartic form of strength $3$ in the closure of the strength at most $2$ locus, answering a question of Ballico--Bik--Oneto--Ventura in the negative. In the analogous setting of partition rank as introduced by Naslund, we further show that the locus of tensors of partition rank at most $2$ is closed, but the locus of tensors of partition rank at most $3$ is not. Together with a suspension lemma, this answers for all $r$ whether the locus of forms/tensors of strength/partition rank at most $r$ is Zariski-closed.
Source: arXiv (Cornell University)
Authors: Baily, Benjamin, Danelon, Alessandro
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223213800