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arXiv · 2502.13545

Mirror symmetry for certain blowups of Grassmannians

Jianxun Hu·Huazhong Ke·Changzheng Li·Lei Song
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Abstract

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 $QH^*(X_{2, n})$.

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Jianxun Hu, Huazhong Ke, Changzheng Li, Lei Song. 2025-02-19. Mirror symmetry for certain blowups of Grassmannians. https://arxiv.org/abs/2502.13545

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