Structure of node polynomials for curves on surfaces
type: Item
instance of: scholarly article
title: Structure of node polynomials for curves on surfaces
zbMATH Open document ID: 1327.14035
author: Nikolay Qviller
published in: Mathematische Nachrichten
publication date: 2014-10-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1102.2092
Mathematics Subject Classification ID: 14C17
Mathematics Subject Classification ID: 05A18
zbMATH DE Number: 6353329
zbMATH Keywords: Göttsche formulas
zbMATH Keywords: nodal curve locus
zbMATH Keywords: multisingularity formulas
MaRDI profile type: Publication
OpenAlex ID: W2950760879
arXiv ID: 1102.2092
cites work: Some characteristic numbers for nodal and cuspidal plane curves of any degree
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cites work: Multisingularities, cobordisms, and enumerative geometry
cites work: Intersection Theory of Moduli Space of Stable N-Pointed Curves of Genus Zero
cites work: Multiple-point formulas. I: Iteration
cites work: A short proof of the Göttsche conjecture
cites work: THE DI FRANCESCO–ITZYKSON–GÖTTSCHE CONJECTURES FOR NODE POLYNOMIALS OF ℙ2
cites work: A proof of the Göttsche-Yau-Zaslow formula
DOI: 10.1002/MANA.201200265
review text: For a smooth projective surface \(S\) and a linear system \(|L|\) let \(N_r\) be the degree of the locus of \(r\)-nodal curves. It is known from the Göttsche conjecture that \(N_r\) is a polynomial of the four relevant numbers of the situation. An earlier paper of the author proves that \(r!N_r=P_r(a_1,\ldots,a_r)\) where \(P_r\) is the \(r\)th complete exponential Bell polynomial and \(a_i\) are universal integer coefficient linear polynomials of the four numbers.NEWLINENEWLINEIn this paper, the author gives an intersection theoretic interpretation of the \(a_i\) linear forms. In addition the relation of the results with \textit{M. È. Kazaryan}'s [Russ. Math. Surv. 58, No. 4, 665--724 (2003); translation from Usp. Mat. Nauk 58, No. 4, 29--88 (2003; Zbl 1062.58039)] multi-singularity formulas is discussed.
reviewed by: Richárd Rimányi
description: scientific article; zbMATH DE number 6353329