109 citations · 289 across the 23 of their papers we have counts for
10 papers · 1 filter
Tropical Poincaré bundle, Fourier-Mukai transform, and a generalized Poincaré formula
Soham Ghosh, Farbod Shokrieh
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 analogu…
Jumps in the height of the Ceresa cycle
Robin de Jong, Farbod Shokrieh
We study the jumps in the archimedean height of the Ceresa cycle, as introduced by R. Hain in his work on normal functions on moduli spaces of curves, and as further analyzed by P.…
Tautological cycles on tropical Jacobians
Andreas Gross, Farbod Shokrieh
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 analo…
Cycles, cocycles, and duality on tropical manifolds
Andreas Gross, Farbod Shokrieh
We prove a Poincaré duality for the Chow rings of smooth fans whose support are tropical linear spaces. As a consequence, we show that cycles and cocycles on tropical manifolds are…
A sheaf-theoretic approach to tropical homology
Andreas Gross, Farbod Shokrieh
We introduce a sheaf-theoretic approach to tropical homology, especially for tropical homology with potentially non-compact supports. Our setup is suited to study the functorial pr…
Tropical moments of tropical Jacobians
Robin de Jong, Farbod Shokrieh
Each metric graph has canonically associated to it a polarized real torus called its tropical Jacobian. A fundamental real-valued invariant associated to each polarized real torus…
Faltings height and Néron-Tate height of a theta divisor
Robin de Jong, Farbod Shokrieh
We prove a formula, which, given a principally polarized abelian variety over the field of algebraic numbers, relates the stable Faltings height of with the Néron--Tate…
Effective divisor classes on metric graphs
Andreas Gross, Farbod Shokrieh, Lilla Tóthmérész
We introduce the notion of semibreak divisors on metric graphs (tropical curves) and prove that every effective divisor class (of degree at most the genus) has a semibreak divisor…
Canonical measures on metric graphs and a Kazhdan's theorem
Farbod Shokrieh, Chenxi Wu
We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of "hyperbolic measures" on universal covers of met…
Non-Archimedean and tropical theta functions
Tyler Foster, Joseph Rabinoff, Farbod Shokrieh +1
We define a tropicalization procedure for theta functions on abelian varieties over a non-Archimedean field. We show that the tropicalization of a non-Archimedean theta function is…