{
  "id": "1310.3685",
  "version": "v2",
  "published": "2013-10-14T13:45:25.000Z",
  "updated": "2015-05-13T17:45:14.000Z",
  "title": "Aeppli Cohomology Classes Associated with Gauduchon Metrics on Compact Complex Manifolds",
  "authors": [
    "Dan Popovici"
  ],
  "comment": "37 pages, to appear in Bulletin de la Soci\\'et\\'e Math\\'ematique de France (accepted in July 2014), acknowledgments added",
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV"
  ],
  "abstract": "We propose the study of a Monge-Amp\\`ere-type equation in bidegree $(n-1,\\,n-1)$ rather than $(1,\\,1)$ on a compact complex manifold $X$ of dimension $n$ for which we prove uniqueness of the solution subject to positivity and normalisation restrictions. Existence will hopefully be dealt with in future work. The aim is to construct a special Gauduchon metric uniquely associated with any Aeppli cohomology class of bidegree $(n-1,\\,n-1)$ lying in the Gauduchon cone of $X$ that we hereby introduce as a subset of the real Aeppli cohomology group of type $(n-1,\\,n-1)$ and whose first properties we study. Two directions for applications of this new equation are envisaged: to moduli spaces of Calabi-Yau $\\partial\\bar\\partial$-manifolds and to a further study of the deformation properties of the Gauduchon cone beyond those given in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-14T13:45:25.000Z",
      "comment": "37 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-13T17:45:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact complex manifold",
      "aeppli cohomology classes",
      "gauduchon metric",
      "real aeppli cohomology group",
      "gauduchon cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3685P"
    }
  }
}