The linear system |D| of a divisor D on a metric graph has the structure of a cell complex. And the set R(D) of corresponding tropical rational functions has the structure of a tropical semimodule. We introduce the anchor divisors and anchor cells in it - they serve as the landmarks for us to compute the f-vector of the complex and find all cells in the complex. Then we compute the minimal set of generators of R(D) using the landmarks. We apply these methods to some examples - namely the canonical linear systems of some small trivalent graphs. Fixing the graph-theoretic type of a metric graph, we discuss the subdivision of the cone of metrics by the combinatorial structure of D.
Speaker(s): Bo Lin (UC Berkeley)