{
  "id": "math/0611002",
  "version": "v1",
  "published": "2006-10-31T22:14:05.000Z",
  "updated": "2006-10-31T22:14:05.000Z",
  "title": "Extremal metrics and K-stability (PhD thesis)",
  "authors": [
    "Gábor Székelyhidi"
  ],
  "comment": "85 pages",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we conjecture to be equivalent to the existence of an extremal metric in the polarisation class. A variant for a complete extremal metric on the complement of a smooth divisor is also given. On toric surfaces we prove a Jordan-Holder type theorem for decomposing semistable surfaces into stable pieces. On a ruled surface we compute the infimum of the Calabi functional for the unstable polarisations, exhibiting a decomposition analogous to the Harder-Narasimhan filtration of an unstable vector bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-31T22:14:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "53C25"
    ],
    "keywords": [
      "phd thesis",
      "k-stability",
      "complete extremal metric",
      "jordan-holder type theorem",
      "geometric invariant theory"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 85,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11002S"
    }
  }
}