On a characterization of an abelian variety in the classification theory of algebraic varieties
Yujiro Kawamata, Eckart Viehweg (1980)
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Yujiro Kawamata, Eckart Viehweg (1980)
Compositio Mathematica
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Leonard Roth (1954)
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Ziv Ran (1980/81)
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Luis Fuentes García (2004)
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We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.
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