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
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.

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

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