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arXiv · 2307.03696

Quantum cohomology of projective bundles

Hiroshi Iritani·Yuki Koto
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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.

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Hiroshi Iritani, Yuki Koto. 2023-07-07. Quantum cohomology of projective bundles. https://arxiv.org/abs/2307.03696

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