Generating series of stable pairs descendent invariants on Fano 3-folds are rational and q ↔ q^{-1} symmetric.
Joyce, Ringel–Hall style Lie algebra structures on the homology of moduli spaces, 2019, preprint available in the author's webpage, https://people.maths.ox.ac.uk/joyce/hall.pdf
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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.