Year: 2025
Type: preprint
Abstract: In this paper, we prove that any Artinian complete intersection homogeneous ideal $I$ in $K[x_0,\cdots,x_n]$ generated by $n+1$ forms of degree $d\ge 2$ satisfies the weak Lefschetz property (WLP) in degree $t< d+\lceil \frac{d}{n} \rceil$. As a consequence, we get that the Jacobian ideal of a smooth 3-fold of degree $d\ge 7$ in ${\mathbb P}^4$ satisfies the weak Lefschetz property in degree $d$, answering a recent question of Beauville.
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979341834
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