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.
Schimpf, Stable pairs on local curves and Bethe roots, 2024, preprint, https://arxiv.org/abs/2409.09508
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Generating series of stable pairs descendent invariants on Fano 3-folds are rational and q ↔ q^{-1} symmetric.
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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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Rationality and symmetry of stable pairs generating series of Fano 3-folds
Generating series of stable pairs descendent invariants on Fano 3-folds are rational and q ↔ q^{-1} symmetric.