{
  "id": "1608.07627",
  "version": "v1",
  "published": "2016-08-26T23:31:56.000Z",
  "updated": "2016-08-26T23:31:56.000Z",
  "title": "On the contravariant of homogeneous forms arising from isolated hypersurface singularities",
  "authors": [
    "Alexander Isaev"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let ${\\mathcal Q}_n^d$ be the vector space of homogeneous forms of degree $d\\ge 3$ on ${\\mathbb C}^n$, with $n\\ge 2$. The object of our study is the map $\\Phi$, introduced in earlier articles by J. Aper, M. Eastwood and the author, that assigns to every form for which the discriminant $\\Delta$ does not vanish the so-called associated form lying in the space ${\\mathcal Q}_n^{n(d-2)*}$. This map is a morphism from the affine variety $X_n^d:=\\{f\\in{\\mathcal Q}_n^d:\\Delta(f)\\ne 0\\}$ to the affine space ${\\mathcal Q}_n^{n(d-2)*}$. Letting $p$ be the smallest integer for which the product $\\Delta^p\\Phi$ extends to a morphism from ${\\mathcal Q}_n^d$ to ${\\mathcal Q}_n^{n(d-2)*}$, one observes that the extended map defines a contravariant of forms in ${\\mathcal Q}_n^d$. In the present paper we obtain upper bounds for $p$ thus providing estimates for the contravariant's degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-26T23:31:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L24",
      "32S25"
    ],
    "keywords": [
      "isolated hypersurface singularities",
      "homogeneous forms arising",
      "extended map defines",
      "contravariants degree",
      "smallest integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}