Node polynomials for curves on surfaces
Abstract
This text is a presentation of a set of formulae, first found by Vainsencher (for δ ≤ 6) and shortly after improved by Kleiman and Piene, counting δ-nodal curves in a complete linear system on a smooth surface, if δ ≤ 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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