Algebraic cycles on generic abelian varieties
Najmuddin Fakhruddin (1996)
Compositio Mathematica
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Najmuddin Fakhruddin (1996)
Compositio Mathematica
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Chad Schoen (1993)
Compositio Mathematica
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Phillip A. Griffiths (1983)
Compositio Mathematica
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James Carlson, Mark Green, Phillip Griffiths, Joe Harris (1983)
Compositio Mathematica
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Cristina Oliva (1994)
Compositio Mathematica
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Fumio Hazama (1994)
Compositio Mathematica
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Claire Voisin (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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. ...