论文标题
plücker坐标镜，用于A型国旗品种
A Plücker coordinate mirror for type A flag varieties
论文作者
论文摘要
我们引入了$ a $ type a $的部分国旗品种的超电势。这是一张$ w：y^\ circ \ to \ mathbb {c} $的地图，其中$ y^\ circ $是格拉斯曼尼亚人产物的反民主分裂的补充。地图$ w $是根据格拉曼尼亚因素的plücker坐标表示的。这种结构概括了沼泽 - 帕尔曼族的摩西式坐标镜子。我们表明，在$ y $的杰出群集图中，我们的超电球与Eguchi-Hori-xiong和Batyrev-ciocan-fontanine-kim-kim- van Strate构建的早期镜子一致。我们的主要工具是标志品种上的量子舒伯特演算。
We introduce a superpotential for partial flag varieties of type $A$. This is a map $W: Y^\circ \to \mathbb{C}$, where $Y^\circ$ is the complement of an anticanonical divisor on a product of Grassmannians. The map $W$ is expressed in terms of Plücker coordinates of the Grassmannian factors. This construction generalizes the Marsh--Rietsch Plücker coordinate mirror for Grassmannians. We show that in a distinguished cluster chart for $Y$, our superpotential agrees with earlier mirrors constructed by Eguchi--Hori--Xiong and Batyrev--Ciocan-Fontanine--Kim--van Straten. Our main tool is quantum Schubert calculus on the flag variety.
