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.
Oberdieck, Towards refined curve counting on the Enriques surface I: K-theoretic refinements , ArXiv:2407.21318, 2024
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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.