2024/04/28 by Mineev, Dmitry
#05B35 #14C17 #14T15 (Primary) #18A10 (Secondary) #52B40 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2404.18127
We prove that the proper amalgam of matroids M1 and M2 along their common restriction N exists if and only if the tropical fibre product of Bergman fans B(M1) ×B(N) B(M2) is positive. We introduce tropical correspondences between Bergman fans as tropical subcycles in their product, similar to correspondences in algebraic geometry, and define a "graph correspondence" of the map of lattices. We prove that graph construction is a functor for the "covering" maps of lattices, exploiting a generalization of Bergman fan which we call a "Flag fan".