Hodge type of projective varieties of low degree
type: Item
instance of: scholarly article
title: Hodge type of projective varieties of low degree
zbMATH Open document ID: 0784.14003
DOI: 10.1007/BF01444698
author: Madhav V. Nori
author: Hélène Esnault
author: V. Srinivas
published in: Mathematische Annalen
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/164940
review text: The paper is devoted to the proof of the following result [conjectured by \textit{P. Deligne} and \textit{A. Dimca} in Ann. Sci. Éc. Norm. Supér., IV. Sér. 23, No. 4, 645-656 (1990; Zbl 0743.14028)]: Let \(S\) be a complex projective variety defined in the \(n\)-dimensional projective space by equations of degrees \(d_ 1\geq\cdots\geq d_ r\). Then the Hodge type of \(S\) is at least the integral part of \[ (n-d_ 2-\cdots-d_ r)/d_ 1. \] Two proofs of this fact are given: one based on Nori's deformation theoretic technique and another inspired from \textit{T. Terasoma}'s use of the ``universal pencil'' [cf. Ann. Math., II. Ser. 132, 213-235 (1990; Zbl 0732.14005)].
reviewed by: Alexandru Buium
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14C34
zbMATH DE Number: 126336
zbMATH Keywords: Hodge type
MaRDI profile type: Publication
cites work: Q5682420
cites work: Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières
cites work: Hodge type of subvarieties of \(\mathbb{P}^ n\) of small degrees
cites work: Algebraic cycles and Hodge theoretic connectivity
cites work: Infinitesimal variation of Hodge structures and the weak global Torelli theorem for complete intersections
OpenAlex ID: W2007218938
description: scientific article; zbMATH DE number 126336