English

Node polynomials for curves on surfaces

Algebraic Geometry 2025-10-09 v1

Abstract

This text is a presentation of a set of formulae, first found by Vainsencher (for δ6\delta \leq 6) and shortly after improved by Kleiman and Piene, counting δ\delta-nodal curves in a complete linear system on a smooth surface, if δ8\delta \leq 8 and the corresponding line bundle is sufficiently positive. We also discuss a complement by Qviller, and related results due to Kazarian, Ohmoto, and others.

Keywords

Cite

@article{arxiv.2510.06839,
  title  = {Node polynomials for curves on surfaces},
  author = {Thomas Dedieu},
  journal= {arXiv preprint arXiv:2510.06839},
  year   = {2025}
}