{
  "id": "2011.08093",
  "version": "v1",
  "published": "2020-11-16T16:49:04.000Z",
  "updated": "2020-11-16T16:49:04.000Z",
  "title": "A Plücker coordinate mirror for type A flag varieties",
  "authors": [
    "Elana Kalashnikov"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "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 Pl\\\"ucker coordinates of the Grassmannian factors. This construction generalizes the Marsh--Rietsch Pl\\\"ucker 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-16T16:49:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J33",
      "14N35"
    ],
    "keywords": [
      "plücker coordinate mirror",
      "flag variety",
      "quantum schubert calculus",
      "partial flag varieties",
      "main tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}