Standard surfaces and nodal curves in symplectic 4-manifolds
arXiv:math/0407494
Abstract
Continuing the program of math.SG/0012067 and math.SG/0310450, 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.
Technical details needed for the proofs of some results in Section 3 have been added in Section 6. 43 pages