{
  "id": "1406.1713",
  "version": "v2",
  "published": "2014-06-06T15:39:22.000Z",
  "updated": "2014-11-17T12:37:31.000Z",
  "title": "On the irreducible components of moduli schemes for affine spherical varieties",
  "authors": [
    "Roman Avdeev",
    "Stéphanie Cupit-Foutou"
  ],
  "comment": "v2 32 pages; v2 generalizes the results obtained in v1 to any finitely generated and saturated monoid",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We give a combinatorial description of the irreducible components of Alexeev and Brion's moduli scheme parameterizing affine spherical varieties with prescribed weight monoid. Furthermore, we prove that these irreducible components are affine spaces. As a consequence of these results, we obtain that the so-called root monoid of any affine spherical variety is free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-06T15:39:22.000Z",
      "title": "On the irreducible components of some moduli schemes for affine multiplicity-free varieties",
      "abstract": "We give a combinatorial description of the irreducible components of Alexeev and Brion's moduli schemes parameterizing affine multiplicity-free varieties with prescribed weight monoid~$\\Gamma$. Furthermore, if $\\Gamma$ is saturated, we prove that the corresponding moduli scheme is irreducible and smooth. If $\\Gamma$ is free, we show that the irreducible components of the moduli scheme are smooth. As a consequence of these results, we derive that the so-called root monoid of an affine spherical variety is free whenever so is its weight monoid.",
      "comment": "19 pages, preliminary version",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-17T12:37:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "irreducible components",
      "moduli schemes parameterizing affine multiplicity-free",
      "schemes parameterizing affine multiplicity-free varieties",
      "brions moduli schemes parameterizing affine"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1713A"
    }
  }
}