The Ceresa period from tropical homology

Ritter, Caelan 

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e112

Résumé

The Jacobian of a very general complex algebraic curve of genus at least 3 contains an algebraic cycle called the Ceresa cycle that is homologically trivial but algebraically nontrivial. Zharkov defined in analogy the tropical Ceresa cycle of a metric graph and proved a similar result for very general tropical curves overlying the complete graph on four vertices. We extend this result by considering a related, ‘universal’ invariant of the underlying graph called the Ceresa period; we show that having trivial Ceresa period has a forbidden minor characterization that coincides with the graph being of hyperelliptic type.

Détail

DOI : 10.1017/fms.2025.10071

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