The refined K-theoretic DT and PT theories of local curves are solved explicitly via localization to skew nested Hilbert schemes, yielding three universal series from the equivariant vertex and confirming the DT/PT correspondence in arbitrary genus.
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Logarithmic topological recursion supplies dilaton equations and free-energy definitions that match the Nekrasov-Shatashvili perturbative partition function and all-genus mirror-curve free energies directly.
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The refined local Donaldson-Thomas theory of curves
The refined K-theoretic DT and PT theories of local curves are solved explicitly via localization to skew nested Hilbert schemes, yielding three universal series from the equivariant vertex and confirming the DT/PT correspondence in arbitrary genus.
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Geometry of Logarithmic Topological Recursion: Dilaton Equations, Free Energies and Variational Formulas
Logarithmic topological recursion supplies dilaton equations and free-energy definitions that match the Nekrasov-Shatashvili perturbative partition function and all-genus mirror-curve free energies directly.