Completion of Katz-Qin-Ruan's Enumeration of Genus-Two Plane Curves

We give a formula for the number of genus-two fixed-complex-structure degree-d plane curves passing through 3d-2 points in general position. This is achieved by completing Katz-Qin-Ruan’s approach. This paper’s formula agrees with the one obtained by the author in a completely different way.