{
  "id": "1409.2969",
  "version": "v1",
  "published": "2014-09-10T06:44:55.000Z",
  "updated": "2014-09-10T06:44:55.000Z",
  "title": "Finiteness of (-2)-reflective lattices of signature (2,n)",
  "authors": [
    "Shouhei Ma"
  ],
  "categories": [
    "math.AG",
    "math.NT",
    "math.QA",
    "math.RT"
  ],
  "abstract": "A modular form for an even lattice L of signature (2,n) is said to be (-2)-reflective if its zero divisor is set-theoretically contained in the Heegner divisor defined by the (-2)-vectors in L. We prove that there are only finitely many even lattices with n>6 which admit (-2)-reflective modular forms. In particular, there is no such lattice in n>29. A similar, but weaker finiteness result is also obtained for n=4, 5, 6. This gives an answer to a weak version of Gritsenko-Nikulin's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-10T06:44:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55",
      "17B67",
      "11F22",
      "14J28"
    ],
    "keywords": [
      "modular form",
      "weaker finiteness result",
      "zero divisor",
      "gritsenko-nikulins conjecture",
      "weak version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.2969M"
    }
  }
}