{
  "id": "2005.04406",
  "version": "v1",
  "published": "2020-05-09T09:50:23.000Z",
  "updated": "2020-05-09T09:50:23.000Z",
  "title": "Invariants of limit key polynomials",
  "authors": [
    "Maria Alberich-Carramiñana",
    "Alberto F. Boix",
    "Julio Fernández",
    "Jordi Guàrdia",
    "Enric Nart",
    "Joaquim Roé"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $\\nu$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with coefficients in a field $K$. We prove comparison theorems between MacLane-Vaqui\\'e key polynomials for valuations $\\mu\\le\\nu$ and abstract key polynomials for $\\nu$. Also, some results on invariants attached to limit key polynomials are obtained. In particular, if $\\operatorname{char}(K)=0$ we show that all limit key polynomials of unbounded continuous MacLane chains have numerical character equal to one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-09T09:50:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial",
      "invariants",
      "arbitrary rank",
      "comparison theorems",
      "unbounded continuous maclane chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}