Hodge numbers of hypersurfaces
type: Item
instance of: scholarly article
title: Hodge numbers of hypersurfaces
zbMATH Open document ID: 0879.14018
DOI: 10.1007/BF02940815
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1997-03-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 977877
zbMATH Keywords: hypersurface
zbMATH Keywords: isolated singularities
zbMATH Keywords: primitive cohomology groups
zbMATH Keywords: mixed Hodge structure
zbMATH Keywords: Euler characteristic
zbMATH Keywords: real points
author: Alexandru Dimca
reviewed by: Fumio Hazama
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 977877