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 ) and shortly after improved by Kleiman and Piene, counting -nodal curves in a complete linear system on a smooth surface, if and the corresponding line bundle is sufficiently positive. We also discuss a complement by Qviller, and related results due to Kazarian, Ohmoto, and others.
Cite
@article{arxiv.2510.06839,
title = {Node polynomials for curves on surfaces},
author = {Thomas Dedieu},
journal= {arXiv preprint arXiv:2510.06839},
year = {2025}
}