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arXiv · 1501.03261

Curves in Hilbert modular varieties

Erwan Rousseau·Frédéric Touzet
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Abstract

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 Green-Griffiths-Lang conjecture for Hilbert modular varieties up to finitely many possible exceptions.

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Erwan Rousseau, Frédéric Touzet. 2015-01-14. Curves in Hilbert modular varieties. https://arxiv.org/abs/1501.03261

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