Mirror symmetry for certain blowups of Grassmannians
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929720086495232 |
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| author | Hu, Jianxun Ke, Huazhong Li, Changzheng Song, Lei |
| author_facet | Hu, Jianxun Ke, Huazhong Li, Changzheng Song, Lei |
| contents | We classify when the blowup of a complex Grassmannian $G(k, n)$ along a smooth Schubert subvariety $Z$ is Fano. We compute almost all the two-point, genus zero Gromov-Witten invariants of the blowup when $Z=G(k, n-1)$. We further prove a mirror symmetry statement for the blowup $X_{2, n}$
of $G(2, n)$ along $G(2, n-1)$, by introducing a toric superpotential $f_{\rm tor}$ and showing the isomorphism between the Jacobi ring of $f_{\rm tor}$ and the small quantum cohomology ring $QH^*(X_{2, n})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mirror symmetry for certain blowups of Grassmannians Hu, Jianxun Ke, Huazhong Li, Changzheng Song, Lei Algebraic Geometry 14N35 We classify when the blowup of a complex Grassmannian $G(k, n)$ along a smooth Schubert subvariety $Z$ is Fano. We compute almost all the two-point, genus zero Gromov-Witten invariants of the blowup when $Z=G(k, n-1)$. We further prove a mirror symmetry statement for the blowup $X_{2, n}$ of $G(2, n)$ along $G(2, n-1)$, by introducing a toric superpotential $f_{\rm tor}$ and showing the isomorphism between the Jacobi ring of $f_{\rm tor}$ and the small quantum cohomology ring $QH^*(X_{2, n})$. |
| title | Mirror symmetry for certain blowups of Grassmannians |
| topic | Algebraic Geometry 14N35 |
| url | https://arxiv.org/abs/2502.13545 |