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, p. 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
@article{ASNSP_2004_5_3_3_637_0,
     author = {Voisin, Claire},
     title = {A geometric application of Nori's connectivity theorem},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {3},
     year = {2004},
     pages = {637-656},
     zbl = {1110.14008},
     mrnumber = {2099253},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2004_5_3_3_637_0}
}
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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