Hodge numbers of hypersurfaces (Q1352274)

Let \(V\) be a hypersurface with isolated singularities in the complex projective space \(\mathbb{P}^{n+1}\). Then there are two possibly nontrivial primitive cohomology groups of \(V\), namely \(H^n_0 (V)\) and \(H_0^{n+1} (V)\), each of which carries a canonical mixed Hodge structure. It is the (mixed) Hodge numbers of \(H^n_0(V)\) that the author compute in terms of some data connected with the singularity of \(V\). As applications, he gives certain formulas which express its Hodges numbers, when \(V\) is a \(\mathbb{Q}\)-manifold, and when all the singularities are weighted homogeneous. Furthermore, he obtains bounds for the Euler characteristic of the real points of \(V\), and restrictions on the possible configurations of singularities.