Consider the gradient map associated to any non-constant homogeneous polynomial f ∈ ℂ[ x0 , ..., xn ] of degree d , defined by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\varphi _f = grad (f):D(f) \to \mathbb{P}^n ,(x_0 : \ldots :x_n ) \to (f_0 (x): \ldots :f_n (x))$$ \end{document} where D ( f ) = { x ∈ ℙ n ; f ( x ) ≠ 0} is the principal open set associated to f and fi = ∂f / ∂xi . This map corresponds to polar Cremona transformations. In Proposition 3.4 we give a new lower bound for the degree d ( f ) of ϕ f under the assumption that the projective hypersurface V : f = 0 has only isolated singularities. When d ( f ) = 1, Theorem 4.2 yields very strong conditions on the singularities of V .