Tautological cycles on tropical Jacobians

Abstract

The classical Poincaré formula relates the rational homology classes of tautological cycles on a Jacobian to powers of the class of Riemann theta divisor. We prove a tropical analogue of this formula. Along the way, we prove several foundational results about real tori with integral structures (and, therefore, tropical abelian varieties). For example, we prove a tropical version of the Appell-Humbert theorem. We also study various notions of equivalences between tropical cycles and their relation to one another.

Cited by in corpus (3)

• Kirchhoff's theorem for Prym varieties
• Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology class
• The Ceresa period from tropical homology