Virasoro Constraints for Toric Bundles

Abstract

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 non-equivariant limit in this formula, using Brown's mirror theorem for toric bundles.

v1: 24 pages; v2: 25 pages, revised expositions. Final version to appear in Forum of Mathematics, Pi

References in corpus (1)

• Permutation-equivariant quantum K-theory VIII. Explicit reconstruction

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