{
  "id": "math/0702834",
  "version": "v1",
  "published": "2007-02-27T14:20:00.000Z",
  "updated": "2007-02-27T14:20:00.000Z",
  "title": "Geometry of the Kimura 3-parameter model",
  "authors": [
    "Marta Casanellas",
    "Jesus Fernandez-Sanchez"
  ],
  "comment": "26 pages with 4 figures",
  "categories": [
    "math.AG",
    "math.AC",
    "q-bio.PE"
  ],
  "abstract": "The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric quotient of the affine space by a finite group acting on it. As a consequence, we are able to study the singularities of W and prove that the biologically meaningful points are smooth points. Then we give an algorithm for constructing a set of minimal generators of the localized ideal at these points, for an arbitrary number of leaves n. This leads to a major improvement of phylogenetic reconstruction methods based on algebraic geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-27T14:20:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92D15",
      "14J99",
      "05C85"
    ],
    "keywords": [
      "affine algebraic variety",
      "phylogenetic reconstruction methods",
      "algebraic geometry",
      "toric variety",
      "geometric quotient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2834C"
    }
  }
}