The Hodge conjecture for a certain class of singular varieties
type: Item
instance of: scholarly article
title: The Hodge conjecture for a certain class of singular varieties
zbMATH Open document ID: 0871.14007
DOI: 10.1007/PL00004283
author: James D. Lewis
published in: Mathematische Zeitschrift
publication date: 1997-07-03T00:00:00Z
review text: Let \(X\) be a reduced separated algebraic scheme over the complex numbers. One can consider a formulation of the general Hodge conjecture (GHC) for \(X\), which extends the formulation of the GHC for smooth projective varieties (Grothendieck's amendment). In this paper, we exhibit examples of \(X\), specifically a class of hypersurfaces, where the GHC holds. The main technical ingredient is the specialization of the diagonal class \(\Delta\) on the ``generic fiber'' of a family \(\overline{\mathcal X}\to T\) to a closed fiber \(\overline X\), and to apply known results about the decomposability of \(\Delta\) for our special class of varieties.
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 1028138
zbMATH Keywords: singular varieties
zbMATH Keywords: generic fiber of a family of hypersurfaces
zbMATH Keywords: decomposability of diagonal class
zbMATH Keywords: general Hodge conjecture
Wikidata QID: Q123017664
MaRDI profile type: Publication
full work available at URL: pl00004283
OpenAlex ID: W1970515505
description: scientific article; zbMATH DE number 1028138