Geodesic
Virasoro constraints for stable pairs on toric threefolds
Forum of Mathematics, Pi, Tome 10 (2022)

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Using new explicit formulas for the stationary Gromov–Witten/Pandharipande–Thomas ($\mathrm {GW}/{\mathrm {PT}}$) descendent correspondence for nonsingular projective toric threefolds, we show that the correspondence intertwines the Virasoro constraints in Gromov–Witten theory for stable maps with the Virasoro constraints for stable pairs proposed in [18]. Since the Virasoro constraints in Gromov–Witten theory are known to hold in the toric case, we establish the stationary Virasoro constraints for the theory of stable pairs on toric threefolds. As a consequence, new Virasoro constraints for tautological integrals over Hilbert schemes of points on surfaces are also obtained. 
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Miguel Moreira; Alexei Oblomkov; Andrei Okounkov; Rahul Pandharipande. Virasoro constraints for stable pairs on toric threefolds. Forum of Mathematics, Pi, Tome 10 (2022). doi: 10.1017/fmp.2022.4

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