Continuing the program of S. Donaldson and I. Smith, and M. Usher, we introduce refinements of the Donaldson-Smith standard surface count which are designed to count nodal pseudoholomorphic curves and curves with a prescribed decomposition into reducible components. In cases where a corresponding analogue of the Gromov-Taubes invariant is easy to define, our invariants agree with those analogues. We also prove a vanishing result for some of the invariants that count nodal curves.
"Standard surfaces and nodal curves in symplectic 4-manifolds." J. Differential Geom. 77 (2) 237 - 290, October 2007. https://doi.org/10.4310/jdg/1191860395