Discrete Mathematics & Theoretical Computer Science 
A tropical curve $\Gamma$ is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system $D$ of a divisor $D$ on a tropical curve $\Gamma$ analogously to the classical counterpart. We investigate the structure of $D$ as a cell complex and show that linear systems are quotients of tropical modules, finitely generated by vertices of the cell complex. Using a finite set of generators, $D$ defines a map from $\Gamma$ to a tropical projective space, and the image can be modified to a tropical curve of degree equal to $\mathrm{deg}(D)$. The tropical convex hull of the image realizes the linear system $D$ as a polyhedral complex.
Source : ScholeXplorer
IsRelatedTo ARXIV 1001.2774 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.aim.2012.02.019 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1001.2774
