Weak Lefschetz property of equigenerated complete intersections: Applications
Abstract
In this paper, we prove that any Artinian complete intersection homogeneous ideal I I in K [ x 0 , ⋯ , x n ] K[x_{0},\cdots ,x_{n}] generated by n + 1 n+1 forms of degree d ≥ 2 d\ge 2 satisfies the weak Lefschetz property (WLP) in degree t > d + ⌈ d n ⌉ t> d+\lceil \frac {d}{n} \rceil . As a consequence, we get that the Jacobian ideal of a smooth 3-fold of degree d ≥ 6 d\ge 6 in P 4 \mathbb {P}^{4} satisfies the weak Lefschetz property in degree d d , answering a recent question of Beauville [ Hyperplane sections of cubic threefolds , Proc. Amer. Math. Soc. 153 (2025), no. 12, 5167–5170].
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Tensor decomposition and applications
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 3
- Pages
- 905–912
- Publication date
- 14 January 2026
- Language
- EN