Tropical curves of hyperelliptic type

TL;DR

This paper introduces tropical curves of hyperelliptic type, characterizing them via graph properties and providing an excluded minors classification, thus advancing understanding of their structure in tropical geometry.

Contribution

It defines hyperelliptic type for tropical curves and offers a graph-theoretic characterization through excluded minors, a novel approach in tropical geometry.

Findings

Hyperelliptic tropical curves are characterized by their underlying graphs.

The property of being hyperelliptic type is minor-closed.

An excluded minors characterization for hyperelliptic type tropical curves is established.

Abstract

We introduce the notion of tropical curves of hyperelliptic type. These are tropical curves whose Jacobian is isomorphic to that of a hyperelliptic tropical curve, as polarized tropical abelian varieties. We show that this property depends only on the underlying graph of a tropical curve and is preserved when passing to genus $\geq 2$ connected minors. The main result is an excluded minors characterization of tropical curves of hyperelliptic type.