On an example of quiver DT/relative GW correspondence

TL;DR

This paper generalizes a recent result connecting quiver Donaldson-Thomas invariants and Gromov-Witten theory, extending it to all genera and refined invariants through degeneration and blow-up techniques.

Contribution

It introduces a broader framework linking quiver DT invariants and Gromov-Witten invariants, including all genera and refined invariants, via geometric degeneration methods.

Findings

Unified the DT/GW correspondence for all genera

Refined the correspondence with more detailed invariants

Extended the result to a broader class of quivers

Abstract

We explain and generalize a recent result of Reineke-Weist by showing how to reduce it to the Gromov-Witten/Kronecker correspondence by a degeneration and blow-up. We also refine the result by working with all genera on the Gromov-Witten side and with refined Donaldson-Thomas invariants on the quiver side.