Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus

Xin Lü; Shengli Tan; Kang Zuo

doi:10.1007/s11425-024-2360-1

Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus

Xin Lü
, Shengli Tan
, Kang Zuo^*

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

We show that there does not exist any Shimura curve with a strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4.

Original language	English
Journal	Science China Mathematics
DOIs	https://doi.org/10.1007/s11425-024-2360-1
State	Accepted/In press - 2025

Keywords

14E30
14J10
Coleman-Oort conjecture
Shimura curve
fibred surface

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10.1007/s11425-024-2360-1

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title = "Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus",

abstract = "We show that there does not exist any Shimura curve with a strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4.",

keywords = "14E30, 14J10, Coleman-Oort conjecture, Shimura curve, fibred surface",

author = "Xin L{\"u} and Shengli Tan and Kang Zuo",

note = "Publisher Copyright: {\textcopyright} Science China Press 2025.",

year = "2025",

doi = "10.1007/s11425-024-2360-1",

language = "英语",

journal = "Science China Mathematics",

issn = "1674-7283",

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AU - Lü, Xin

AU - Tan, Shengli

AU - Zuo, Kang

N1 - Publisher Copyright: © Science China Press 2025.

PY - 2025

Y1 - 2025

N2 - We show that there does not exist any Shimura curve with a strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4.

AB - We show that there does not exist any Shimura curve with a strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus g ≽ 4.

KW - 14E30

KW - 14J10

KW - Coleman-Oort conjecture

KW - Shimura curve

KW - fibred surface

UR - https://www.scopus.com/pages/publications/85217205458

U2 - 10.1007/s11425-024-2360-1

DO - 10.1007/s11425-024-2360-1

M3 - 文章

AN - SCOPUS:85217205458

SN - 1674-7283

JO - Science China Mathematics

JF - Science China Mathematics

ER -

Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus

Abstract

Keywords

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