English

Virasoro Constraints for Toric Bundles

Algebraic Geometry 2024-02-13 v2

Abstract

We show that the Virasoro conjecture in Gromov--Witten theory holds for the the total space of a toric bundle EBE \to B if and only if it holds for the base BB. The main steps are: (i) we establish a localization formula that expresses Gromov--Witten invariants of EE, equivariant with respect to the fiberwise torus action, in terms of genus-zero invariants of the toric fiber and all-genus invariants of BB; and (ii) we pass to the non-equivariant limit in this formula, using Brown's mirror theorem for toric bundles.

Keywords

Cite

@article{arxiv.1508.06282,
  title  = {Virasoro Constraints for Toric Bundles},
  author = {Tom Coates and Alexander Givental and Hsian-Hua Tseng},
  journal= {arXiv preprint arXiv:1508.06282},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-22T10:41:25.887Z