Virasoro constraints for stable pairs on toric 3-folds

Abstract

Using new explicit formulas for the stationary GW/PT descendent correspondence for nonsingular projective toric 3-folds, we show that the correspondence intertwines the Virasoro constraints in Gromov-Witten theory for stable maps with the Virasoro constraints for stable pairs. 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 3-folds. As a consequence, new Virasoro constraints for tautological integrals over Hilbert schemes of points on surfaces are also obtained.

arXiv comment65 pages

References in corpus (7)

• Curve counting via stable pairs in the derived category
• The structure of 2D semi-simple field theories
• Quantum Cohomology and Virasoro Algebra
• Virasoro constraints and the Chern classes of the Hodge bundle
• Three questions in Gromov-Witten theory
• 13/2 ways of counting curves
• Gromov-Witten/Pairs descendent correspondence for toric 3-folds

Cited by in corpus (2)

• Virasoro conjecture for the stable pairs descendent theory of simply connected 3-folds (with applications to the Hilbert scheme of points of a surface)
• Virasoro constraints in quantum singularity theories