The set of forms with bounded strength is not closed

@article{Ballico2022TheSO,
  title={The set of forms with bounded strength is not closed},
  author={Edoardo Ballico and Arthur Bik and A. Oneto and Emanuele Ventura},
  journal={Comptes Rendus. Math{\'e}matique},
  year={2022}
}
The strength of a homogeneous polynomial (or form) $f$ is the smallest length of an additive decomposition expressing it whose summands are reducible forms. We show that the set of forms with bounded strength is not always Zariski-closed. In particular, if the ground field has characteristic $0$, we prove that the set of quartics with strength $\leq3$ is not Zariski-closed for a large number of variables. 

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