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<p>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 <i>g</i> ≽ 4. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus <i>g</i> ≽ 4.</p>

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

  • 期刊论文

  • 发表日期：

    2025年1月7日

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  • Xin Lü,
  • Shengli Tan,
  • Kang Zuo

摘要

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.