Computing linear systems on metric graphs

Abstract

The linear system |D| of a divisor D on a metric graph has the structure of a cell complex. 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. A linear system can also be identified as a tropical convex hull of rational functions. We compute its extremal generators using the landmarks. We apply these methods to some examples – namely the canonical linear systems of some small trivalent graphs.