The set of forms with bounded strength is not closed
Algebraic Geometry
2022-05-02 v2 Commutative Algebra
Representation Theory
Abstract
The strength of a homogeneous polynomial (or form) is the smallest length of an additive decomposition expressing it whose summands are reducible forms. Using polynomial functors, we show that the set of forms with bounded strength is not always Zariski-closed. More specifically, if the ground field is algebraically closed, we prove that the set of quartics with strength is not Zariski-closed for a large number of variables.
Keywords
Cite
@article{arxiv.2012.01237,
title = {The set of forms with bounded strength is not closed},
author = {Edoardo Ballico and Arthur Bik and Alessandro Oneto and Emanuele Ventura},
journal= {arXiv preprint arXiv:2012.01237},
year = {2022}
}
Comments
9 pages, removed condition on characteristic