The tropical Abel–Prym map
Abstract
We prove that, under mild assumptions, the tropical Abel–Prym map Ψ : Γ ˜ → Prym ( Γ ˜ / Γ ) associated with a free double cover π : Γ ˜ → Γ is harmonic of degree 2 if and only if the source graph Γ ˜ is hyperelliptic. This is in accordance with the already established algebraic result. In this case, the Abel–Prym graph Ψ ( Γ ˜ ) is hyperelliptic of genus g Γ - 1 and its Jacobian is isomorphic, as a pptav, to the Prym variety of the cover. We further show that the Abel–Prym graph coincides with a connected component of the tropical bigonal construction. En route, we count the number of distinct free double covers by hyperelliptic metric graphs.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Advanced Algebra and Geometry
Holomorphic and Operator Theory
Publication details
- Journal / source
- Algebraic Combinatorics
- Volume
- 8
- Issue
- 6
- Pages
- 1493–1527
- Publication date
- 6 January 2026
- Language
- EN