{
  "id": "hep-th/9901089",
  "version": "v3",
  "published": "1999-01-20T17:22:19.000Z",
  "updated": "1999-05-05T02:45:45.000Z",
  "title": "Hilbert Schemes, Separated Variables, and D-Branes",
  "authors": [
    "A. Gorsky",
    "N. Nekrasov",
    "V. Rubtsov"
  ],
  "comment": "harvmac, 27 pp. big mode; v2. typos and references corrected",
  "journal": "Commun.Math.Phys. 222 (2001) 299-318",
  "doi": "10.1007/s002200100503",
  "categories": [
    "hep-th"
  ],
  "abstract": "We explain Sklyanin's separation of variables in geometrical terms and construct it for Hitchin and Mukai integrable systems. We construct Hilbert schemes of points on $T^{*}\\Sigma$ for $\\Sigma = {\\IC}, {\\IC}^{*}$ or elliptic curve, and on ${\\bf C}^{2}/{\\Gamma}$ and show that their complex deformations are integrable systems of Calogero-Sutherland-Moser type. We present the hyperk\\\"ahler quotient constructions for Hilbert schemes of points on cotangent bundles to the higher genus curves, utilizing the results of Hurtubise, Kronheimer and Nakajima. Finally we discuss the connections to physics of $D$-branes and string duality.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-05-05T02:45:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "separated variables",
      "explain sklyanins separation",
      "higher genus curves",
      "construct hilbert schemes",
      "cotangent bundles"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2001,
      "volume": 222,
      "number": 2,
      "pages": 299
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 495033,
      "adsabs": "2001CMaPh.222..299G"
    }
  }
}