Geodesic
Node Polynomials for Curves on Surfaces
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $r$ ordinary nodes. The second part is proved here. It asserts that, for $r\le 8$, 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.
Keywords: enumerative geometry, nodal curves, nodal polynomials, Bell polynomials, Enriques diagrams, Hilbert schemes. 
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Steven Kleiman; Ragni Piene. Node Polynomials for Curves on Surfaces. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a58/

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