Node Polynomials for Curves on Surfaces

Symmetry Integrability and Geometry-Methods and Applications

article

Steven Kleiman¹  Ragni Piene² 

[1] Room 2-172, Department of Mathematics;Department of Mathematics, University of Oslo

关键词: enumerative geometry;    nodal curves;    nodal polynomials;    Bell polynomials;    Enriques diagrams;    Hilbert schemes.;   

DOI  :  10.3842/SIGMA.2022.059

来源: National Academy of Science of Ukraine

【 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 $r\le 8$, 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.

【 授权许可】

Unknown