Tautological cycles on tropical Jacobians
Algebraic Geometry
2023-05-03 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1910.07165,
title = {Tautological cycles on tropical Jacobians},
author = {Andreas Gross and Farbod Shokrieh},
journal= {arXiv preprint arXiv:1910.07165},
year = {2023}
}