Double spaces with isolated singularities

Abstract

We prove the non-rationality of a double cover of ${\mathbb{P}}^n$ branched over a hypersurface $F\subset {\mathbb{P}}^n$ of degree $2n$ having isolated singularities such that $n\ge 4$ and every singular points of the hypersurface $F$ is ordinary, i.e. the projectivization of its tangent cone is smooth, whose multiplicity does not exceed $2(n-2)$.

References in corpus (2)

• Essentials of the method of maximal singularities
• A sextic surface cannot have 66 nodes

Cited by in corpus (1)

• On factoriality of nodal threefolds