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 ≤ 3 is not Zariski-closed for a large number of variables.
The set of forms with bounded strength is not closed / Ballico, Edoardo; Bik, Arthur; Oneto, Alessandro; Ventura, Emanuele. - In: COMPTES RENDUS. MATHÉMATIQUE. - ISSN 1778-3569. - 360:G4(2022), pp. 371-380. [10.5802/crmath.302]
The set of forms with bounded strength is not closed
Ballico, Edoardo;Oneto, Alessandro;
2022-01-01
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 ≤ 3 is not Zariski-closed for a large number of variables.| File | Dimensione | Formato | |
|---|---|---|---|
|
2012.01237.pdf
accesso aperto
Tipologia:
Post-print referato (Refereed author’s manuscript)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
191.97 kB
Formato
Adobe PDF
|
191.97 kB | Adobe PDF | Visualizza/Apri |
|
CRMATH_2022__360_G4_371_0.pdf
accesso aperto
Tipologia:
Versione editoriale (Publisher’s layout)
Licenza:
Creative commons
Dimensione
571.1 kB
Formato
Adobe PDF
|
571.1 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
