The paper proves Vafa-Intriligator formulas for genus zero quasimap invariants of smooth semi-positive GIT quotients V//G by reducing them to toric computations via abelianization.
Log Calabi-Yau surfaces and Jeffrey-Kirwan residues
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abstract
We prove an equality, predicted in the physical literature, between the Jeffrey-Kirwan residues of certain explicit meromorphic forms attached to a quiver without loops or oriented cycles and its Donaldson-Thomas type invariants. In the special case of complete bipartite quivers we also show independently, using scattering diagrams and theta functions, that the same Jeffrey-Kirwan residues are determined by the the Gross-Hacking-Keel mirror family to a log Calabi-Yau surface.
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A Vafa-Intriligator formula for semi-positive quotients of linear spaces
The paper proves Vafa-Intriligator formulas for genus zero quasimap invariants of smooth semi-positive GIT quotients V//G by reducing them to toric computations via abelianization.