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, Valentina; Miró-Roig, Rosa. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - STAMPA. - Volume 154, Number 3:(2026), pp. 905-912. [Epub ahead of print] [10.1090/proc/17508]
Weak Lefschetz property of equigenerated complete intersections: Applications
Beorchia, Valentina
Membro del Collaboration Group
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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].Pubblicazioni consigliate
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