Tropical Poincaré bundle, Fourier-Mukai transform, and a generalized Poincaré formula

2025/03/17 by Ghosh, Soham, Shokrieh, Farbod · 1 citation
#11G10 #14C17 #14C25 #14C40 #14H40 #14T20 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.12835

Abstract

We construct a tropical analogue of the Poincaré bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analogue of Beauville's generalized Poincaré formula for polarized abelian varieties. Some consequences include a geometric Riemann-Roch theorem for tropical abelian varieties, as well as a tropical Poincaré-Prym formula which was recently conjectured by Röhrle and Zakharov.

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• Topology and Euler characteristics of tropical varieties

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