A mirror theorem for non-split toric bundles
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909229739147264 |
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| author | Koto, Yuki |
| author_facet | Koto, Yuki |
| contents | We construct an I-function for toric bundles obtained as a fiberwise GIT quotient of a (not necessarily split) vector bundle. This is a generalization of Brown's I-function for split toric bundles and the I-function for non-split projective bundles. In order to prove the mirror theorem, we establish a characterization of points on the Givental Lagrangian cones of toric bundles and prove a mirror theorem for the twisted Gromov-Witten theory of a fiber product of projective bundles. The former result generalizes Brown's characterization for split toric bundles to the non-split case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09888 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A mirror theorem for non-split toric bundles Koto, Yuki Algebraic Geometry Symplectic Geometry We construct an I-function for toric bundles obtained as a fiberwise GIT quotient of a (not necessarily split) vector bundle. This is a generalization of Brown's I-function for split toric bundles and the I-function for non-split projective bundles. In order to prove the mirror theorem, we establish a characterization of points on the Givental Lagrangian cones of toric bundles and prove a mirror theorem for the twisted Gromov-Witten theory of a fiber product of projective bundles. The former result generalizes Brown's characterization for split toric bundles to the non-split case. |
| title | A mirror theorem for non-split toric bundles |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2310.09888 |