Forum of Mathematics, Sigma (Jan 2024)

The Ceresa class and tropical curves of hyperelliptic type

  • Daniel Corey,
  • Wanlin Li

DOI
https://doi.org/10.1017/fms.2024.36
Journal volume & issue
Vol. 12

Abstract

Read online

We define a new algebraic invariant of a graph G called the Ceresa–Zharkov class and show that it is trivial if and only if G is of hyperelliptic type, equivalently, G does not have as a minor the complete graph on four vertices or the loop of three loops. After choosing edge lengths, this class specializes to an algebraic invariant of a tropical curve with underlying graph G that is closely related to the Ceresa cycle for an algebraic curve defined over $\mathbb {C}(\!(t)\!)$ .

Keywords