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arXiv · 1709.03627

Automorphism groups of superspecial curves of genus $4$ over $\mathbb{F}_{11}$

Momonari Kudo·Shushi Harashita·Hayato Senda
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Abstract

In this paper, we explicitly determine the automorphism group of every nonhyperelliptic superspecial curve of genus $4$ over $\mathbb{F}_{11}$. Our algorithm determining automorphism groups works for any nonhyperelliptic curves of genus $4$ over finite fields. With this computation, we show the compatibility between the enumeration of superspecial curves of genus $4$ over $\mathbb{F}_{11}$ obtained computationally by the first and second authors in 2017 and an enumeration by Galois cohomology theory.

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Momonari Kudo, Shushi Harashita, Hayato Senda. 2017-09-11. Automorphism groups of superspecial curves of genus $4$ over $\mathbb{F}_{11}$. https://doi.org/10.1016/j.jpaa.2020.106339

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