Correspondence theorems for tropical curves

In this paper, we study the correspondence between tropical curves and holomorphic curves. The main subjects in this paper are superabundant tropical curves. First we give an effective combinatorial description of these curves. Based on this description, we calculate the obstructions for appropriate deformation theory, describe the Kuranishi map, and study the solution space of it. The genus one case is solved completely, and the theory works for many of the higher genus cases, too.