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Density of the Noether- Lefschetz locus for the hyperplane sections of Calabi-Yau threefolds. (Densité du lieu de Noether-Lefschetz pour les sections hyperplanes des variétés de Calabi-Yau de dimension 3.) (French) Zbl 0772.14015
The subject of this paper is related with the problem of studying the image of the Abel-Jacobi map for a projective manifold $$X$$. In a previous paper the author proved that it has infinite rank when $$X$$ is a generic hypersurface of degree 5 in $$\mathbb{P}^ 4$$, and a fundamental step in the proof was the density of the irreducible components of maximal codimension of the Noether-Lefschetz locus $$S(U)$$, where $$U\subseteq\mathbb{P}(H^ 0({\mathcal O}_ X(1)))$$ parametrizes the smooth hyperplane sections of $$X$$. The same result is established here for a Calabi-Yau 3-fold $$X$$ and for $$U\subseteq\mathbb{P}(H^ 0({\mathcal O}_ X(n)))$$ $$(n\gg 0)$$. In this case the density statement is reduced to the study of a system of quadrics in $$\mathbb{P}(H^ 0({\mathcal O}_ \Sigma(n)))$$ for a generic $$\Sigma\in U$$.

##### MSC:
 14J30 $$3$$-folds 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14C22 Picard groups 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) 14D07 Variation of Hodge structures (algebro-geometric aspects)
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