Curves of genus two with maps of every degree to a fixed elliptic curve
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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Mathematics and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Document type
- Preprint