The non-unit gradient degree conjecture for hypersurfaces with isolated singularities

Let $f\in \mathbb{C}[x_0,\ldots,x_n]$ be a reduced homogeneous polynomial, and let $V(f)$ be its associated projective hypersurface. Write $d=\operatorname{deg}(f)$ and let $d(f)$ denote the degree of the gradient map of $f$. Assume

$$d>2,\qquad n>2,$$

and that $V(f)$ has only isolated singularities. Non-unit gradient degree conjecture. Then

$$d(f)\neq 1.$$

This conjecture concerns the degree of the gradient map for projective hypersurfaces with isolated singularities and asserts that, beyond the quadratic and low-dimensional cases, this degree cannot equal one. Its resolution status is not specified in the supplied text.