The Ceresa class and tropical curves of hyperelliptic type

2022/04/13 by Corey, Daniel, Li, Wanlin
#14T25 (primary) 57K20 (secondary) #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2204.06316

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 4 vertices or the loop of 3 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 ℂ( (t) ).

Related

• The Ceresa class: tropical, topological, and algebraic
• The Ceresa period from tropical homology
• A non-hyperelliptic curve with torsion Ceresa cycle modulo algebraic equivalence
• A non-hyperelliptic curve with torsion Ceresa class
• Tropical curves of hyperelliptic type