Quantum cohomology of projective bundles

Fuente: arXiv
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Main Authors: Iritani, Hiroshi, Koto, Yuki
Format: Preprint
Published: 2023
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author Iritani, Hiroshi
Koto, Yuki
author_facet Iritani, Hiroshi
Koto, Yuki
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_03696
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Quantum cohomology of projective bundles
Iritani, Hiroshi
Koto, Yuki
Algebraic Geometry
Symplectic Geometry
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.
title Quantum cohomology of projective bundles
topic Algebraic Geometry
Symplectic Geometry
url https://arxiv.org/abs/2307.03696