{
  "id": "1206.4925",
  "version": "v2",
  "published": "2012-06-21T16:06:42.000Z",
  "updated": "2013-04-03T22:08:47.000Z",
  "title": "Stabilization of monomial maps in higher codimension",
  "authors": [
    "Jan-Li Lin",
    "Elizabeth Wulcan"
  ],
  "comment": "16 pages, to appear in the Annales de l'Institut Fourier",
  "categories": [
    "math.DS",
    "math.AG"
  ],
  "abstract": "A monomial self-map $f$ on a complex toric variety is said to be $k$-stable if the action induced on the $2k$-cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of $f$, we can find a toric model with at worst quotient singularities where $f$ is $k$-stable. If $f$ is replaced by an iterate one can find a $k$-stable model as soon as the dynamical degrees $\\lambda_k$ of $f$ satisfy $\\lambda_k^2>\\lambda_{k-1}\\lambda_{k+1}$. On the other hand, we give examples of monomial maps $f$, where this condition is not satisfied and where the degree sequences $\\deg_k(f^n)$ do not satisfy any linear recurrence. It follows that such an $f$ is not $k$-stable on any toric model with at worst quotient singularities.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-03T22:08:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monomial maps",
      "higher codimension",
      "worst quotient singularities",
      "toric model",
      "stabilization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.4925L"
    }
  }
}