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We study (rational) sweeping out of general hypersurfaces by varieties having small moduli spaces. As a consequence, we show that general -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.
@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},
pages = {637--656},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 3},
number = {3},
year = {2004},
mrnumber = {2099253},
zbl = {1110.14008},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_3_637_0/}
}
TY - JOUR AU - Voisin, Claire TI - A geometric application of Nori's connectivity theorem JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 637 EP - 656 VL - 3 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_3_637_0/ LA - en ID - ASNSP_2004_5_3_3_637_0 ER -
%0 Journal Article %A Voisin, Claire %T A geometric application of Nori's connectivity theorem %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 637-656 %V 3 %N 3 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_3_637_0/ %G en %F 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, Série 5, Tome 3 (2004) no. 3, pp. 637-656. http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_3_637_0/