Node Polynomials for Curves on Surfaces
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS(2022)
摘要
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 < 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.
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关键词
enumerative geometry, nodal curves, nodal polynomials, Bell polynomials, En-riques diagrams, Hilbert schemes
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