{
  "id": "1312.6797",
  "version": "v2",
  "published": "2013-12-24T11:25:39.000Z",
  "updated": "2014-10-02T06:29:04.000Z",
  "title": "Spaces of algebraic maps from real projective spaces to toric varieties",
  "authors": [
    "Andrzej Kozlowski",
    "Masahiro Ohno",
    "Kohhei Yamaguchi"
  ],
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "The problem of approximating the infinite dimensional space of all continuous maps from an algebraic variety $X$ to an algebraic variety $Y$ by finite dimensional spaces of algebraic maps arises in several areas of geometry and mathematical physics. An often considered formulation of the problem (sometimes called the Atiyah-Jones problem after \\cite{AJ}) is to determine a (preferably optimal) integer $n_D$ such that the inclusion from this finite dimensional algebraic space into the corresponding infinite dimensional one induces isomorphisms of homology (or homotopy) groups through dimension $n_D$, where $D$ denotes a tuple of integers called the \"degree\" of the algebraic maps and $n_D\\to\\infty$ as $D\\to\\infty$. In this paper we investigate this problem in the case when $X$ is a real projective space and $Y$ is a smooth compact toric variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-24T11:25:39.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-02T06:29:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D99",
      "14M25"
    ],
    "keywords": [
      "real projective space",
      "algebraic variety",
      "finite dimensional algebraic space",
      "smooth compact toric variety",
      "finite dimensional spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6797K"
    }
  }
}