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.
Révisé le :
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Edoardo Ballico 1 ; Arthur Bik 2 ; Alessandro Oneto 1 ; Emanuele Ventura 3
CC-BY 4.0
@article{CRMATH_2022__360_G4_371_0,
author = {Edoardo Ballico and Arthur Bik and Alessandro Oneto and Emanuele Ventura},
title = {The set of forms with bounded strength is not closed},
journal = {Comptes Rendus. Math\'ematique},
pages = {371--380},
publisher = {Acad\'emie des sciences, Paris},
volume = {360},
year = {2022},
doi = {10.5802/crmath.302},
language = {en},
}
TY - JOUR AU - Edoardo Ballico AU - Arthur Bik AU - Alessandro Oneto AU - Emanuele Ventura TI - The set of forms with bounded strength is not closed JO - Comptes Rendus. Mathématique PY - 2022 SP - 371 EP - 380 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.302 LA - en ID - CRMATH_2022__360_G4_371_0 ER -
Edoardo Ballico; Arthur Bik; Alessandro Oneto; Emanuele Ventura. The set of forms with bounded strength is not closed. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 371-380. doi : 10.5802/crmath.302. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.302/
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