Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (3 of 3)
Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University
Curves in Hilbert modular varieties
Pages: 673 – 690
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.
Hilbert-modular varieties, Green–Griffiths–Lang conjecture, entire curves, foliations, Second Main Theorem
2010 Mathematics Subject Classification
Primary 32Q45, 37F75. Secondary 11F41.
Received 3 May 2016
Accepted 1 June 2017
Published 20 September 2018