Quantum cohomology of projective bundles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915763832487936 |
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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 |