2 problems

Let $n\geq 2$ and $d\geq 3$, and let $f\in\mathbb C[x_1,\ldots,x_n]_d$ satisfy … Here $\operatorname{Stab}_{\operatorname{GL}(\mathbb C^n)}(f)$ denotes the stabilizer of $f$, and…

Let $S=\mathbb C[x_1,\ldots,x_n]$ and let $g\in S$ be homogeneous of degree $d\geq 3$, with $n\geq 2$. Assume that its Hessian $H(g)$ is a monomial. Smooth monomial-Hessian conject…