Quantum cohomology of projective bundles
Algebraic Geometry
2026-02-03 v4 Symplectic Geometry
Abstract
We construct an I-function of the projective bundle P(V) associated with a not necessarily split vector bundle V\to B as a Fourier transform of the S^1-equivariant J-function of the total space of V and show that it lies on the Givental Lagrangian cone of P(V). Using this result, we show that the quantum cohomology D-module of P(V) splits into the direct sum of the quantum cohomology D-modules of the base space B. This has applications to the semisimplicity of big quantum cohomology.
Keywords
Cite
@article{arxiv.2307.03696,
title = {Quantum cohomology of projective bundles},
author = {Hiroshi Iritani and Yuki Koto},
journal= {arXiv preprint arXiv:2307.03696},
year = {2026}
}
Comments
40 pages, 2 figures; v2: Figure 2 added, v3: Introducion improved, v4: proof of Theorem 1.1 streamlined, log q term in the change of coordinates for Theorem 1.7 removed, error in Theorem 5.1(5) corrected, a reconstruction algorithm added in Section 5.8