Double spaces with isolated singularities

The non-rationality is proved for double covers of $\mathbb P^n$ branched over a hypersurface $F\subset\mathbb P^n$ of degree $2n\geqslant8$ with isolated singularities such that the multiplicity of each singular point of $F$ does not exceed $2(n-2)$ and the projectivization of its tangent cone is smooth.
Bibliography: 15 titles.