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arXiv · 2510.06839

Node polynomials for curves on surfaces

Thomas Dedieu
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Abstract

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

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Thomas Dedieu. 2025-10-08. Node polynomials for curves on surfaces. https://arxiv.org/abs/2510.06839

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