{
  "id": "math/0602223",
  "version": "v1",
  "published": "2006-02-10T16:57:40.000Z",
  "updated": "2006-02-10T16:57:40.000Z",
  "title": "Relative exactness modulo a polynomial map and algebraic $(\\mathbb{C}^p,+)$-actions",
  "authors": [
    "Philippe Bonnet"
  ],
  "comment": "26 pages",
  "journal": "Bull. Soc. math. France 131 (3), 2003, p. 373-398",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let $F=(f_1,...,f_q)$ be a polynomial dominating map from $\\mathbb{C}^n$ to $\\mathbb{C}^q$. We study the quotient ${\\cal{T}}^1(F)$ of polynomial 1-forms that are exact along the fibres of $F$, by 1-forms of type $dR+\\sum a_idf_i$, where $R,a_1,...,a_q$ are polynomials. We prove that ${\\cal{T}}^1(F)$ is always a torsion $\\mathbb{C}[t_1,...,t_q]$-module. The we determine under which conditions on $F$ we have ${\\cal{T}}^1(F)=0$. As an application, we study the behaviour of a class of algebraic $(\\mathbb{C}^p,+)$-actions on $\\mathbb{C}^n$, and determine in particular when these actions are trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-10T16:57:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R20",
      "14R25"
    ],
    "keywords": [
      "relative exactness modulo",
      "polynomial map",
      "polynomial dominating map",
      "conditions",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2223B"
    }
  }
}