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

Ke Chen; Xin Lu; Kang Zuo

doi:10.1007/s40304-018-0155-8

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

Ke Chen
, Xin Lu
, Kang Zuo^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	249-268
Number of pages	20
Journal	Communications in Mathematics and Statistics
Volume	6
Issue number	3
DOIs	https://doi.org/10.1007/s40304-018-0155-8
State	Published - 1 Sep 2018

Keywords

Coleman-Oort conjecture
Corestriction
Higgs bundles
Shimura curves
Torelli locus

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10.1007/s40304-018-0155-8

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abstract = "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.",

keywords = "Coleman-Oort conjecture, Corestriction, Higgs bundles, Shimura curves, Torelli locus",

author = "Ke Chen and Xin Lu and Kang Zuo",

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AU - Lu, Xin

AU - Zuo, Kang

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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.

AB - 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.

KW - Coleman-Oort conjecture

KW - Corestriction

KW - Higgs bundles

KW - Shimura curves

KW - Torelli locus

UR - https://www.scopus.com/pages/publications/85053182518

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DO - 10.1007/s40304-018-0155-8

M3 - 文章

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SN - 2194-6701

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JO - Communications in Mathematics and Statistics

JF - Communications in Mathematics and Statistics

IS - 3

ER -

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

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Keywords

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