{
  "id": "1303.4495",
  "version": "v3",
  "published": "2013-03-19T06:31:43.000Z",
  "updated": "2014-08-14T01:02:25.000Z",
  "title": "Equidistribution in Higher Codimension for Holomorphic Endomorphisms of $\\mathbb{P}^k$",
  "authors": [
    "Taeyong Ahn"
  ],
  "comment": "Corrected an error in the statement of the main theorem and readability has been improved. This paper is based on the work in arXiv:math/0703702 and arXiv:0901.3000 by other authors; for precise estimates, we go over the proofs with modification",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "In this paper, we discuss the equidistribution phenomena for holomorphic endomorphisms over $\\mathbb{P}^k$ in the case of bidegree $(p,p)$ with $1<p<k$. We prove that if $f:\\mathbb{P}^k\\to\\mathbb{P}^k$ is a holomorphic endomorphism of degree $d\\geq 2$ and $T^p$ denotes the Green $(p,p)$-current associated with $f$, then there exists a proper invariant analytic subset $E$ for $f$ such that $d^{-pn}(f^n)^*(S)\\to T^p$ exponentially fast in the current sense for every positive closed $(p,p)$-current $S$ of mass 1 such that $S$ is smooth on $E$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-14T01:02:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "holomorphic endomorphism",
      "higher codimension",
      "proper invariant analytic subset",
      "equidistribution phenomena",
      "current sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4495A"
    }
  }
}