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Tautological cycles on tropical Jacobians

Andreas Gross and Farbod Shokrieh

Vol. 17 (2023), No. 4, 885–921

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.

Poincare formula, tropical curve, Jacobian, tropical homology
Mathematical Subject Classification
Primary: 14H40, 14H42, 14H51, 14T10
Received: 20 October 2020
Revised: 1 May 2022
Accepted: 6 July 2022
Published: 2 May 2023
Andreas Gross
Institut für Mathematik
Goethe-Universität Frankfurt
Farbod Shokrieh
Department of Mathematics
University of Washington
Seattle, WA
United States

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