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arXiv · 1910.07165

Tautological cycles on tropical Jacobians

Andreas Gross·Farbod Shokrieh
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Abstract

The classical Poincar\'e 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.

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Andreas Gross, Farbod Shokrieh. 2019-10-16. Tautological cycles on tropical Jacobians. https://doi.org/10.2140/ant.2023.17.885

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