On the value of thinking tropically to understand Ionel's GW invariants   relative normal crossing divisors
  Ionel's GW invariants relative normal-crossing divisors appear different from Gromov-Witten invariants defined using log schemes or exploded manifolds. Appearances are, in this case, deceiving. I sketch the relationship between Ionel's invariants and their exploded cousins using the example of the moduli space of lines in the complex projective plane relative two coordinate lines. Even in this simplest of examples, 13 different types of curves appear in Ionel's compactified moduli space, but these different types of curves can be understood in a unified and intuitive fashion using tropical curves. 
Brett Parker
math.SG