Local GW invariants of elliptic multiple fibers (Q1940450)

The main goal of the paper is the calculation of the local dimension-zero Gromov-Witten invariants of the multiple fibres of an elliptic surface. This completes the calculations started by the author and \textit{T. H. Parker} [J. Differ. Geom. 77, No. 3, 483--513 (2007; Zbl 1130.53059)], of all dimension-zero Gromov-Witten invariants of minimal elliptic surfaces with \(p_g > 0\). The paper unde review makes heavy use of the computations in that paper, so that it might make sense for a non-expert to study them simultaneously. Calculations for the regular fibre and the multiple fibre of multiplicity \(2\) were already carried out in [the author and \textit{T. H. Parker}, loc. cit.]. In that case the situation is generic (which basically means that the contribution of each point in the moduli space of stable maps to the Gromov-Witten invariant can be computed directly). In the higher-multiplicity case this is no longer true, and the main computation of this paper is a perturbation of the non-generic part of the situation to a generic one, which allows to complete the whole calculation.