Tropical Poincar\'e bundle, Fourier-Mukai transform, and a generalized Poincar\'e formula
Algebraic Geometry
2025-03-18 v1 Combinatorics
Abstract
We construct a tropical analogue of the Poincar\'e bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analogue of Beauville's generalized Poincar\'e formula for polarized abelian varieties. Some consequences include a geometric Riemann-Roch theorem for tropical abelian varieties, as well as a tropical Poincar\'e-Prym formula which was recently conjectured by R\"ohrle and Zakharov.
Cite
@article{arxiv.2503.12835,
title = {Tropical Poincar\'e bundle, Fourier-Mukai transform, and a generalized Poincar\'e formula},
author = {Soham Ghosh and Farbod Shokrieh},
journal= {arXiv preprint arXiv:2503.12835},
year = {2025}
}