Abstract
We describe a correspondence between the Donaldson-Thomas enu- merating D0-D6 bound states on a Calabi-Yau 3-fold and certain Gromov-Witten invari- ants counting rational curves in a family of blowups of weighted projective planes. This is a variation on a correspondence found by Gross-Pandharipande, with D0-D6 bound states replacing representations of generalised Kronecker quivers. We build on a small part of the theories developed by Joyce-Song and Kontsevich-Soibelman for wall-crossing for- mulae and by Gross-Pandharipande-Siebert for factorisations in the tropical vertex group. Along the way we write down an explicit formula for the BPS state counts which arise up to rank 3 and prove their integrality. We also compare with previous noncommutative DT invariants computations in the physics literature.
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