Hodge numbers of hypersurfaces
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.
scientific article; zbMATH DE number 977877
scientific article