Théorème de Torelli pour les cubiques de \({\mathbb{P}}^ 5\). (Torelli theorem for the cubics of \({\mathbb{P}}^ 5)\)
type: Item
instance of: scholarly article
title: Théorème de Torelli pour les cubiques de \({\mathbb{P}}^ 5\). (Torelli theorem for the cubics of \({\mathbb{P}}^ 5)\)
zbMATH Open document ID: 0622.14009
DOI: 10.1007/BF01389270
author: Claire Voisin
published in: Inventiones Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143409
review text: On prouve le théorème suivant: ''Soient X et X' deux cubiques lisses de \({\mathbb{P}}^ 5({\mathbb{C}})\), et soit i une isométrie \(H^ 4(X,{\mathbb{Z}})\to H^ 4(X',{\mathbb{Z}})\) préservant la classe \(h^ 2\) d'une section linéaire et induisant un isomorphisme de structures de Hodge \(i\otimes {\mathbb{C}}: H^ 4(X,{\mathbb{C}})\to H^ 4(X',{\mathbb{C}}).\) Il existe alors un isomorphisme \(I: X'\to X\) induisant i.'' La cubique de \({\mathbb{P}}^ 5\) est une des exceptions au résultat général de Donagi sur le théorème de Torelli pour les hypersurfaces [\textit{R. Donagi}, Compos. Math. 50, 325-353 (1983; Zbl 0598.14007)]. La démonstration utilise la variété de droites contenues dans une cubique de \({\mathbb{P}}^ 5\).
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 14J35
zbMATH DE Number: 4008542
zbMATH Keywords: cubic fourfold
zbMATH Keywords: Hodge structure
zbMATH Keywords: Torelli problem
zbMATH Keywords: variety of lines
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4008542