{
  "id": "math/0610473",
  "version": "v1",
  "published": "2006-10-16T07:10:05.000Z",
  "updated": "2006-10-16T07:10:05.000Z",
  "title": "Poincare series of a toric variety",
  "authors": [
    "Ann Lemahieu"
  ],
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "For an affine toric variety X we compute the Poincare series of the multi-index filtration defined by a finite number of monomial divisorial valuations on the ring O_{X,0}. We give an alternative description of the Poincare series as an integral with respect to the Euler characteristic over the projectivization of the space of germs O_{X,0}. In particular we study divisorial valuations on the ring O_{C^d,0} that arise by considering toric constellations. We give an explicit formula for the Poincare series and a nice geometric description. This generalizes an expression of the Poincare series for curves and rational surface singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-16T07:10:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05"
    ],
    "keywords": [
      "poincare series",
      "monomial divisorial valuations",
      "affine toric variety",
      "study divisorial valuations",
      "nice geometric description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10473L"
    }
  }
}