{
  "id": "1603.01877",
  "version": "v1",
  "published": "2016-03-06T20:55:23.000Z",
  "updated": "2016-03-06T20:55:23.000Z",
  "title": "Algebraic dimension of complex nilmanifolds",
  "authors": [
    "Anna Fino",
    "Gueo Grantcharov",
    "Misha Verbitsky"
  ],
  "comment": "21 pages",
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV"
  ],
  "abstract": "Let M be a complex nilmanifold, that is, a compact quotient of a nilpotent Lie group endowed with an invariant complex structure by a discrete lattice. A holomorphic differential on M is a closed, holomorphic 1-form. We show that $a(M)\\leq k$, where $a(M)$ is the algebraic dimension $a(M)$ (i.e. the transcendence degree of the field of meromorphic functions) and $k$ is the dimension of the space of holomorphic differentials. We prove a similar result about meromorphic maps to Kahler manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-06T20:55:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex nilmanifold",
      "algebraic dimension",
      "holomorphic differential",
      "nilpotent lie group",
      "invariant complex structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160301877F"
    }
  }
}