Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Composantes de petite codimension du lieu de Noether-Lefschetz: Un argument asymptotique en faveur de la conjecture de Hodge pour les hypersurfaces


Author: Ania Otwinowska
Journal: J. Algebraic Geom. 12 (2003), 307-320
DOI: https://doi.org/10.1090/S1056-3911-02-00349-1
Published electronically: November 14, 2002
MathSciNet review: 1949646
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Abstract | References | Additional Information

Abstract:

This paper gives an asymptotic description of the Noether-Lefschetz locus for smooth projective hypersurfaces in $\mathbb {P}^{2n+1}_{\mathbb {C}}$ of large degree. I prove that successive small codimensional components of this locus correspond to surfaces containing a small degree subvariety of dimension $n$. This result generalises the work of Green and Voisin for surfaces in $\mathbb {P}^3_{\mathbb {C}}$ containing a line and a conic.

Résumé Cet article donne une description asymptotique du lieu de Noether-Lefschetz pour les hypersurfaces lisses de grand degré dans $\mathbb {P}^{2n+1}_{\mathbb {C}}$: les composantes succéssives de plus petite codimension de ce lieu sont constituées par les hypersurfaces contenant une sous-variété de dimension $n$ et de petit degré. Ce résultat généralise les travaus de Green et Voisin sur les surfaces de $\mathbb {P}^3_{\mathbb {C}}$ contenant une droite et une conique.


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Additional Information

Ania Otwinowska
Affiliation: Mathematical Institute, University of Warwick, Coventry CV4 7AL, England
Address at time of publication: Université Paris-Sud, Bât 425, 91405 Orsay Cedex, France
Email: ania@maths.warwick.ac.uk

Received by editor(s): October 31, 2000
Published electronically: November 14, 2002