{
  "id": "1612.06593",
  "version": "v1",
  "published": "2016-12-20T10:28:56.000Z",
  "updated": "2016-12-20T10:28:56.000Z",
  "title": "Group actions on quiver varieties and applications",
  "authors": [
    "Victoria Hoskins",
    "Florent Schaffhauser"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We study two types of actions on moduli spaces of quiver representations over a field $k$ and we decompose their fixed loci using group cohomology. First, for a perfect field $k$, we study the action of the absolute Galois group of $k$ on the $\\overline{k}$-valued points of this quiver moduli space; the fixed locus is the set of $k$-rational points and we obtain a decomposition of this fixed locus indexed by elements in the Brauer group of $k$. Second, we study algebraic actions of finite groups of quiver automorphisms on these moduli spaces; the fixed locus is decomposed using group cohomology and we give a modular interpretation of each component. As an application, we construct branes in hyperk\\\"ahler quiver varieties, as fixed loci of such actions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-20T10:28:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14L24"
    ],
    "keywords": [
      "quiver varieties",
      "fixed locus",
      "group actions",
      "application",
      "group cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}