{
  "id": "1810.04662",
  "version": "v1",
  "published": "2018-10-10T17:49:11.000Z",
  "updated": "2018-10-10T17:49:11.000Z",
  "title": "Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations",
  "authors": [
    "Jian Xiao"
  ],
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "It is noted that using complex Hessian equations and the concavity inequalities for elementary symmetric polynomials implies a generalized form of Hodge index inequality. Inspired by this result, using G{\\aa}rding's theory for hyperbolic polynomials, we obtain a mixed Hodge-index type theorem for classes of type $(1,1)$. The new feature is that this Hodge-index type theorem holds with respect to mixed polarizations in which some satisfy particular positivity condition, but could be degenerate and even negative along some directions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-10T17:49:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex hessian equations",
      "hodge-index type inequalities",
      "hyperbolic polynomials",
      "hodge-index type theorem holds",
      "elementary symmetric polynomials implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}