Local GW Invariants of Elliptic Multiple Fibers

TL;DR

This paper calculates the local Gromov-Witten invariants for elliptic multiple fibers using geometric methods, completing the understanding of all dimension zero invariants for elliptic surfaces with positive geometric genus.

Contribution

It introduces a straightforward geometric approach to compute local GW invariants of elliptic fibers, filling a gap in the classification of invariants for elliptic surfaces.

Findings

Calculated local GW invariants for elliptic multiple fibers.

Completed the classification of all dimension zero GW invariants for elliptic surfaces with p_g>0.

Provided geometric arguments simplifying previous computations.

Abstract

We use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with $p_g>0$.