{
  "id": "math/0002097",
  "version": "v2",
  "published": "2000-02-14T18:49:54.000Z",
  "updated": "2000-08-01T20:19:41.000Z",
  "title": "Calibrated Fibrations on Complete Manifolds via Torus Action",
  "authors": [
    "Edward Goldstein"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we will investigate torus actions on complete manifolds with calibrations. For Calabi-Yau manifolds M^2n with a Hamiltonian structure-preserving k-torus action we show that any symplectic reduction has a natural holomorphic volume form. Moreover Special Lagrangian (SLag) submanifolds of the reduction lift to SLag submanifolds of M, invariant under the torus action. If k=n-1 and the first cohomology of M is trivial, then we prove that M is a fibration with generic fiber being a SLag submanifold. As an application we will see that crepant resolutions of singularities of a finite Abelian subgroup of SU(n) acting on C^n have SLag fibrations. We study SLag submanifolds on the total space K(N) of a canonical bundle of a Kahler-Einstein manifold N with positive scalar curvature. We give a conjecture about fibration of K(N) by SLag subvarieties with a certain asymptotic behavior at infinity, which we prove if N is toric. We also get similar results for coassociative submanifolds of a G_2-manifold M^7, which admits a 3-torus, a 2-torus or an SO(3)-action.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-08-01T20:19:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete manifolds",
      "calibrated fibrations",
      "natural holomorphic volume form",
      "hamiltonian structure-preserving k-torus action",
      "finite abelian subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......2097G"
    }
  }
}