标题： 格拉斯曼流形的某些爆破的镜像对称性 显示英文标题

标题： Mirror symmetry for certain blowups of Grassmannians

摘要： 我们分类当复数Grassmannian $G(k, n)$ 沿着一个光滑的Schubert子簇 $Z$ 进行爆破时是否为Fano流形。 当 $Z=G(k, n-1)$ 时，我们计算几乎所有的两点、零亏格Gromov-Witten不变量。 我们进一步通过引入一个toric超势能$f_{\rm tor}$并证明$f_{\rm tor}$的Jacobi环与小量子上同调环$QH^*(X_{2, n})$之间的同构，证明了沿$G(2, n-1)$对$G(2, n)$进行爆破后的镜像对称性陈述$X_{2, n}$。 显示英文摘要

摘要： 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 $QH^*(X_{2, n})$.