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arXiv · 2601.19050

Curves of genus two with maps of every degree to a fixed elliptic curve

Everett W. Howe
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Abstract

We show that up to isomorphism there are exactly twenty pairs $(C,E)$, where $C$ is a genus-$2$ curve over ${\mathbf C}$, where $E$ is an elliptic curve over ${\mathbf C}$, and where for every integer $n>1$ there is a map of degree $n$ from $C$ to $E$. We also show that for every genus-$2$ curve $C$, there is an integer $n$ with $1 < n \le 59$ such that there is no minimal degree-$n$ map from $C$ to an elliptic curve.

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Everett W. Howe. 2026-01-27. Curves of genus two with maps of every degree to a fixed elliptic curve. https://arxiv.org/abs/2601.19050

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