Let $X$ be a nonsingular projective 3-fold. I am trying to understand the proof of the GW/DT correspondence as presented in Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds. I would appreciate if anyone were to explain the general idea behind virtual localization. To be more specific, How the capped localization expresses the primary GW/DT invariants of $X$ as a sum of capped vertex and capped edge data.
Is it possible to explain this in terse statements without going into the details. I believe that this will help my intuition as I try to wade through the detailed contents.