Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (1 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
On Higgs bundles over Shimura varieties of ball quotient type
Pages: 269 – 284
We prove the generic exclusion of certain Shimura varieties of unitary and orthogonal types from the Torelli locus. The proof relies on a slope inequality on surface fibration due to G. Xiao, and the main result implies that certain Shimura varieties only meet the Torelli locus in dimension zero.
Coleman–Oort conjecture, Torelli locus, Shimura varieties, slope inequality
2010 Mathematics Subject Classification
Primary 11G15, 14G35, 14H40. Secondary 14D07, 14K22.
This work is supported by SFB/Transregio 45 Periods, Moduli Spaces and Arithmetic of Algebraic Varieties of the DFG (Deutsche Forschungsgemeinschaft), and by National Key Basic Research Program of China (Grant No. 2013CB834202) and National Natural Science Foundation of China (Grant No. 1171203, No. 11231003, No. 11301495).
Received 21 October 2016
Accepted 2 June 2017
Published 15 June 2018