Tropical linear systems on curves

From CRCG-Wiki

For an effective divisor D on a tropical curve X, we
 identify a finite set of generators of the tropical semimodule

 whose tropical projectivization is the linear system |D| = L(D)/R.

 Using these generators, D defines a map from X to (finite
 dimensional) tropical projective space. The tropical convex hull of
 its image realizes the Gathmann-Kerber/Mikhalkin-Zharkov
 representation of |D| as a polytopal complex.

 This setup allows us to define the notion of (very) ample divisor.
 We show that every divisor of positive degree is ample, and that the
 canonical divisor KX is very ample for sufficiently generic
 curves of genus gX ≥ 3.

 This is work in progress with Gregg Musiker and Josephine Yu (MIT).