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The Set of Forms with Bounded Strength Is Not Closed by Ballico, Edoardo; Bik, Arthur; Oneto, Alessandro; Ventura, Emanuele is a scholarly article available to read on EtoBox.

What is The Set of Forms with Bounded Strength Is Not Closed about?

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 $\leq3$ is not Zariski-closed for a large number of variables.

Author

Ballico, Edoardo; Bik, Arthur; Oneto, Alessandro; Ventura, Emanuele

Published

2020

Language

EN