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Virasoro Constraints for Toric Bundles
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- Journal:
- Forum of Mathematics, Pi / Volume 12 / 2024
- Published online by Cambridge University Press:
- 01 January 2024, e4
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We show that the Virasoro conjecture in Gromov–Witten theory holds for the the total space of a toric bundle
$E \to B$ if and only if it holds for the base B. The main steps are: (i) We establish a localization formula that expresses Gromov–Witten invariants of E, equivariant with respect to the fiberwise torus action in terms of genus-zero invariants of the toric fiber and all-genus invariants of B, and (ii) we pass to the nonequivariant limit in this formula, using Brown’s mirror theorem for toric bundles.
