{
  "id": "1401.0479",
  "version": "v1",
  "published": "2014-01-02T17:35:20.000Z",
  "updated": "2014-01-02T17:35:20.000Z",
  "title": "Rational curves on hyperkahler manifolds",
  "authors": [
    "Ekaterina Amerik",
    "Misha Verbitsky"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $M$ be an irreducible holomorphically symplectic manifold. We show that all faces of the Kahler cone of $M$ are hyperplanes $H_i$ orthogonal to certain homology classes, called monodromy birationally minimal (MBM) classes. Moreover, the Kahler cone is a connected component of a complement of the positive cone to the union of all $H_i$. We provide several characterizations of the MBM-classes. We show the invariance of MBM property by deformations, as long as the class in question stays of type (1,1). For hyperkahler manifolds with Picard group generated by a negative class $z$, we prove that $\\pm z$ is Q-effective if and only if it is an MBM class. We also prove some results towards the Morrison-Kawamata cone conjecture for hyperkahler manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-02T17:35:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperkahler manifolds",
      "rational curves",
      "kahler cone",
      "morrison-kawamata cone conjecture",
      "homology classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0479A"
    }
  }
}