Zhenjian Wang
We prove that a homogeneous 0-dimensional complete intersection satisfies the Strong Lefschetz Property (SLP) in degree 1 if and only if its associated form has nonzero Hessian.
This paper contains 2 theorems, 16 equations.
Theorem 1
Let $M({\bf f})$ be a 0-dimensional homogeneous complete intersection. Then the strong Lefschetz property holds in degree 1 for $M({\bf f})$; that is, for a generic linear form $\ell \in S_1$, the multiplication map is an isomorphism, if and only if the Hessian of its associated form $\mathrm{A}_{\bf f}$ is nonzero.
