Describing tropical curves via algebraic geometry

In this paper, we give a general deformation theoretical set up for the problem of the correspondence between tropical curves and holomorphic curves. Using this formulation, the correspondence theorem for non-superabundant tropical curves is naturally solved. This formulation also gives an effective combinatorial description of the superabundant tropical curves, which will give the basis for the study of correspondence between tropical curves and holomorphic curves for superabundant cases [8].