Sammendrag
We complete the proof of a theorem we announced and partly proved in [Math. Nachr., vol. 271 (2004), Thm. 2.5, p. 74]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper. It describes a natural cycle that enumerates the curves in the family with precisely r ordinary nodes. The second part is proved here. It asserts that, for r≤8, the class of this cycle is given by a computable universal polynomial in the pushdowns to the parameter space of products of the Chern classes of the family.
Node polynomials for curves on surfaces