Node Polynomials for Curves on Surfaces
Algebraic Geometry
2022-08-03 v2
Abstract
We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. 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 ordinary nodes. The second part is proved here. It asserts that, for , 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.
Cite
@article{arxiv.2202.11611,
title = {Node Polynomials for Curves on Surfaces},
author = {Steven Kleiman and Ragni Piene},
journal= {arXiv preprint arXiv:2202.11611},
year = {2022}
}