Une précision concernant le théorème de Noether. (A precision concerning the theorem of Noether)
type: Item
instance of: scholarly article
title: Une précision concernant le théorème de Noether. (A precision concerning the theorem of Noether)
zbMATH Open document ID: 0616.14030
DOI: 10.1007/BF01450079
author: Claire Voisin
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164387
review text: We use the polynomial description of the infinitesimal variation of Hodge structure of hypersurfaces in \({\mathbb{P}}^ n({\mathbb{C}})\) in order to show the following result: Let d be an integer at least five; let \(S_ d\subset {\mathbb{P}}(H^ 0({\mathcal O}_{{\mathbb{P}}^ 3}(d)))\) be the family of smooth surfaces of degree \(d\) such that \(Pic(S_ d)\neq {\mathbb{Z}}\). \(S_ d\) is a countable union of analytic subsets and we have the theorem: Each component of \(S_ d\) is of codimension at least d-3, with equality holding only for the component consisting of surfaces containing a line.
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 3997985
zbMATH Keywords: infinitesimal variation of Hodge structure of hypersurfaces
zbMATH Keywords: family of smooth surfaces
zbMATH Keywords: codimension
MaRDI profile type: Publication
cites work: On the periods of certain rational integrals. I, II
cites work: On the Noether-Lefschetz theorem and some remarks on codimension-two cycles
cites work: Q3697132
cites work: Q3347989
cites work: Q3731740
cites work: Curves on generic hypersurfaces
OpenAlex ID: W2913078127
description: scientific article; zbMATH DE number 3997985