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Curves in Hilbert modular varieties

Erwan Rousseau, Frédéric Touzet
2018 Asian Journal of Mathematics  
We prove a boundedness-theorem for families of abelian varieties with real multiplication. More generally, we study curves in Hilbert modular varieties from the point of view of the Green-Griffiths-Lang conjecture claiming that entire curves in complex projective varieties of general type should be contained in a proper subvariety. Using holomorphic foliations theory, we establish a Second Main Theorem following Nevanlinna theory. Finally, with a metric approach, we establish the strong
more » ... the strong Green-Griffiths-Lang conjecture for Hilbert modular varieties up to finitely many possible exceptions.
doi:10.4310/ajm.2018.v22.n4.a4 fatcat:64r23a5jqbhnlfkyluhqq7m2xy