{
  "id": "1307.1957",
  "version": "v4",
  "published": "2013-07-08T06:30:44.000Z",
  "updated": "2013-07-16T02:48:01.000Z",
  "title": "The Donaldson-Futaki invariant for sequences of test configurations",
  "authors": [
    "Toshiki Mabuchi"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this note, given a polarized algebraic manifold $(X,L)$, we define the Donaldson-Futaki invariant for a sequence of test configurations for $(X,L)$ with exponents tending to infinity. This then allows us to define a strong version of K-stability or K-semistability for $(X,L)$. In particular, $(X,L)$ will be shown to be K-semistable in this strong sense if the polarization class $c_1(L)$ admits a constant scalar curvature Kaehler metric.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-07-16T02:48:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q26",
      "14L24",
      "53C25"
    ],
    "keywords": [
      "test configurations",
      "donaldson-futaki invariant",
      "constant scalar curvature kaehler metric",
      "strong version",
      "polarized algebraic manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1957M"
    }
  }
}