A geometric application of Nori's connectivity theorem
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 637-656.

We study (rational) sweeping out of general hypersurfaces by varieties having small moduli spaces. As a consequence, we show that general $K$-trivial hypersurfaces are not rationally swept out by abelian varieties of dimension at least two. As a corollary, we show that Clemens’ conjecture on the finiteness of rational curves of given degree in a general quintic threefold, and Lang’s conjecture saying that such varieties should be rationally swept-out by abelian varieties, contradict.

Classification: 14C05,  14D07
Voisin, Claire 1

1 Institut de mathématiques de Jussieu CNRS,UMR 7586
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Voisin, Claire. A geometric application of Nori's connectivity theorem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 637-656. http://www.numdam.org/item/ASNSP_2004_5_3_3_637_0/

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