The Oort Conjecture for Shimura Curves of Small Unitary Rank

被引：2

作者：

Chen, Ke ^{[1
]}

Lu, Xin ^{[2
]}

Zuo, Kang ^{[3
]}

机构：

[1] Nanjing Univ, Dept Math, Hankou Rd 22, Nanjing 210093, Jiangsu, Peoples R China

[2] East China Normal Univ, Shanghai Key Lab PMMP, Sch Math Sci, Dongchuan Rd 500, Shanghai 200241, Peoples R China

[3] Johannes Gutenberg Univ Mainz, Inst Math, D-55099 Mainz, Germany

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2018年 / 6卷 / 03期

关键词：

Coleman-Oort conjecture; Torelli locus; Shimura curves; Higgs bundles; Corestriction; VARIETIES;

D O I：

10.1007/s40304-018-0155-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：249 / 268

页数：20

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