Counting curves on elliptic ruled surface
type: Item
instance of: scholarly article
title: Counting curves on elliptic ruled surface
zbMATH Open document ID: 1026.53050
DOI: 10.1016/S0166-8641(01)00235-8
author: Tian-Jun Li
author: Ai-Ko Liu
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: The authors calculate the symplectic Gromov-Witten invariants of \(S^2\times T^2\) by using Kähler structures [cf. \textit{M. Gromov}, Invent. Math. 82, 307-347 (1985; Zbl 0592.53025)]. In alternative terms, the results concern the number of embedded genus \(g\) curves in the homology class \[ A_{\ell, d}=l[S^2]+ d[T^2]. \] The first result determines the number \(N_1(A_{\ell,1})=2\) of embedded genus 1 curves in \(A_{\ell,1}\) passing through \(2\ell\) points. The second result determines the generating function (not stated here) for the number \(N_g(A_{1,d})\) (or \(n_g(A_{1,d})\), resp.) of genus \(g\) curves in class \(A_{1,d}\) passing through \(g+1\) points (passing through \(g\) points and intersecting two circles which generate the first integral homology, respectively).
Mathematics Subject Classification ID: 53D45
zbMATH DE Number: 1879097
zbMATH Keywords: Gromov-Witten invariant
zbMATH Keywords: symplectic form
zbMATH Keywords: symplectic structure
reviewed by: Jan Chrastina
MaRDI profile type: Publication
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full work available at URL: s0166-8641(01)00235-8
OpenAlex ID: W2026302121
description: scientific article; zbMATH DE number 1879097