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arXiv · 1903.08095

The existence of supersingular curves of genus 4 in arbitrary characteristic

Momonari Kudo·Shushi Harashita·Hayato Senda
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Abstract

We prove that there exists a supersingular nonsingular curve of genus $4$ in arbitrary characteristic $p$. For $p>3$ we shall prove that the desingularization of a certain fiber product over $\mathbb{P}^1$ of two supersingular elliptic curves is supersingular.

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Momonari Kudo, Shushi Harashita, Hayato Senda. 2019-03-19. The existence of supersingular curves of genus 4 in arbitrary characteristic. https://doi.org/10.1007/s40993-020-00217-x

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