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