The existence of supersingular curves of genus 4 in arbitrary characteristic

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.

References in corpus (3)

• Newton Polygons Arising for Special Families of Cyclic Covers of the Projective Line
• A note on certain superspecial and maximal curves of genus $5$
• On the existence of superspecial nonhyperelliptic curves of genus $4$