The positive tropicalization of rank 2 matrices

We consider the tropicalization of determinantal varieties of matrices of rank at most 2 and determine which cones correspond to the tropicalization of positive matrices. We give a combinatorial description of this positive part in terms of tropically collinear point configurations, bicolored phylogenetic trees and perfect matchings in bipartite graphs.

This is joint work in progress with Georg Loho and Rainer Sinn.