Linear Systems on Tropical Curves

Understand

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 extended to a tropical curve of degree equal to \deg(D).