{
  "id": "1407.2691",
  "version": "v1",
  "published": "2014-07-10T04:54:38.000Z",
  "updated": "2014-07-10T04:54:38.000Z",
  "title": "Top-stable degenerations of finite dimensional representations II",
  "authors": [
    "H. Derksen",
    "B. Huisgen-Zimmermann",
    "J. Weyman"
  ],
  "journal": "Advances in Math. 259 (2014) 730-765",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let $\\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any semisimple object $T \\in \\Lambda\\text{-mod}$, the class of those $\\Lambda$-modules with fixed dimension vector (say $\\bf d$) and top $T$ which do not permit any proper top-stable degenerations possesses a fine moduli space. This moduli space, $\\mathfrak{ModuliMax}^T_{\\bf d}$, is a projective variety. Despite classifiability up to isomorphism, the targeted collections of modules are representation-theoretically rich: indeed, any projective variety arises as $\\mathfrak{ModuliMax}^T_{\\bf d}$ for suitable choices of $\\Lambda$, $\\bf d$, and $T$. In tandem, we give a structural characterization of the finite dimensional representations that have no proper top-stable degenerations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-10T04:54:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "14D20",
      "16D70",
      "16G20"
    ],
    "keywords": [
      "finite dimensional representations",
      "proper top-stable degenerations possesses",
      "stringent geometric terms",
      "fine moduli space",
      "finite dimensional algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2691D"
    }
  }
}