\(L_ 2\)-cohomology of Kähler varieties with isolated singularities (Q1205535)

Let \(V\) be a complex projective variety with only isolated singularities. Then it is shown that the smooth part \(V_ 0=V\backslash\text{Sing} V\) admits Kähler distinguished metrics such that: (i) the \(L_ 2\)-cohomology of \(V_ 0\) relative to such a metric is isomorphic to the intersection cohomology \(IH^ \bullet(V;\mathbb{C})\) of \(V\); (ii) the corresponding \(L_ 2\)-Hodge structure on \(IH^ \bullet(V;\mathbb{C})\) coincides with the canonical pure Hodge structure given by Morihiko Saito.