The Ceresa class and tropical curves of hyperelliptic type
Daniel Corey,
Wanlin Li
Abstract: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
$\mathbb {C}(\!(t)\!)$
.
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