In this paper, we prove that any Artinian complete intersection homogeneous ideal I in K[x0,··· , xn] generated by n + 1 forms of degree d ≥ 2 satisfies the weak Lefschetz property (WLP) in degree t < d + ⌈d/n ⌉. As a consequence, we get that the Jacobian ideal of a smooth 3-fold of degree d ≥ 6 in P4 satisfies the weak Lefschetz property in degree d, answering a recent question of Beauville [Hyperplane sections of cubic threefolds, Proc. Amer. Math. Soc. 153 (2025), no. 12, 5167–5170].
Weak Lefschetz property of equigenerated complete intersections: Applications / Beorchia, V., Miró-Roig, R.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - STAMPA. - Volume 154:Number 3(2026), pp. 905-912. [10.1090/proc/17508]
Weak Lefschetz property of equigenerated complete intersections: Applications
Beorchia, ValentinaPrimo
Membro del Collaboration Group
;
2026-01-01
Abstract
In this paper, we prove that any Artinian complete intersection homogeneous ideal I in K[x0,··· , xn] generated by n + 1 forms of degree d ≥ 2 satisfies the weak Lefschetz property (WLP) in degree t < d + ⌈d/n ⌉. As a consequence, we get that the Jacobian ideal of a smooth 3-fold of degree d ≥ 6 in P4 satisfies the weak Lefschetz property in degree d, answering a recent question of Beauville [Hyperplane sections of cubic threefolds, Proc. Amer. Math. Soc. 153 (2025), no. 12, 5167–5170].| File | Dimensione | Formato | |
|---|---|---|---|
|
S0002-9939-2026-17508-1.pdf
Accesso chiuso
Tipologia:
Documento in Versione Editoriale
Licenza:
Copyright Editore
Dimensione
182.78 kB
Formato
Adobe PDF
|
182.78 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
