The Oort Conjecture for Shimura Curves of Small Unitary Rank Dedicated to celebrate the Sixtieth anniversary of USTC  

作　　者：Ke Chen Xin Lu Kang Zuo 

机构地区：[1]Department of Mathematics,Nanjing University,Hankou Road 22,Nanjing 210093,People’s Republic of China [2]School of Mathematical Sciences,Shanghai Key Laboratory of PMMP,East China Normal University,Dongchuan Road 500,Shanghai 200241,People’s Republic of China [3]Institut für Mathematik,Universität Mainz,55099 Mainz,Germany

出　　处：《Communications in Mathematics and Statistics》2018年第3期249-268,共20页数学与统计通讯（英文）

基　　金：supported by SFB/Transregio 45 Periods,Moduli Spaces and Arithmetic of Algebraic Varieties of DFG,by NSF of China Grant Nos.11771203,11231003,11301495;Fundamental Research Funds for the Central Universities,Nanjing University,No.0203-14380009;by the Science Foundation of Shanghai(No.13DZ2260400).

摘　　要：We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper bound.As an application we show that the Coleman–Oort conjecture holds for Shimura curves associated with partial corestriction upon a suitable choice of parameters,which generalizes a construction due to Mumford.

关 键 词：Coleman-Oort conjecture Torelli locus Shimura curves Higgs bundles Corestriction 

分 类 号：O15[理学—数学]