Asian Journal of Mathematics

Volume 22 (2018)

Number 2

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

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n2.a4

Authors

Ke Chen (Department of Mathematics, Nanjing University, Nanjing, China)

Xin Lu (School of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China)

Sheng-Li Tan (School of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China)

Kang Zuo (Institut für Mathematik, Universität Mainz, Germany)

Abstract

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.

Keywords

Coleman–Oort conjecture, Torelli locus, Shimura varieties, slope inequality

2010 Mathematics Subject Classification

Primary 11G15, 14G35, 14H40. Secondary 14D07, 14K22.

Full Text (PDF format)

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