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Faltings Heights of Hyperelliptic Curves over Function Fields

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Abstract

Faltings heights over function fields of complex projective curves are modular invariants of families of curves. The question on minimized Faltings heights was raised by Mazur. In this note, we consider this question for a simple class of families of hyperelliptic curves. We obtain a complete result of this question in this case.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P. R. China

    **ao Lei Liu

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  1. **ao Lei Liu
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Correspondence to **ao Lei Liu.

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Conflict of Interest The authors declare no conflict of interest.

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Supported by NSFC (Grant No. 12271073) and Fundamental Research Funds of the Central Universities (Grant No. DUT18RC(4)065)

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Liu, X.L. Faltings Heights of Hyperelliptic Curves over Function Fields. Acta. Math. Sin.-English Ser. 39, 2364–2373 (2023). https://doi.org/10.1007/s10114-023-1690-0

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  • DOI: https://doi.org/10.1007/s10114-023-1690-0

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