The existence of supersingular curves of genus 4 in arbitrary characteristic
2020
We prove that there exists a supersingular nonsingular curve of genus 4 in arbitrary characteristic
$$p>0$$
. For
$$p>3$$
we shall prove that the desingularization of a certain fiber product over
$$\mathbf{P }^1$$
of two supersingular elliptic curves is supersingular.
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