{
  "id": "math/0403464",
  "version": "v4",
  "published": "2004-03-26T15:28:22.000Z",
  "updated": "2006-04-24T20:05:11.000Z",
  "title": "Multiple points in P^2 and degenerations to elliptic curves",
  "authors": [
    "Ivan Petrakiev"
  ],
  "comment": "8 pages; this is a revised version of an earlier draft",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider the problem of bounding the dimension of the linear system of curves in ${\\bf P}^2$ of degree $d$ with prescribed multiplicities $m_1,...,m_n$ at $n$ general points (\\cite{Hir1},\\cite{Hir2}). We propose a new method, based on the work of Ciliberto and Miranda (\\cite {CM1}, \\cite {CM2}), by specializing the general points to an elliptic curve in ${\\bf P}^2$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-04-24T20:05:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H50",
      "14C20"
    ],
    "keywords": [
      "elliptic curve",
      "multiple points",
      "degenerations",
      "general points",
      "linear system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3464P"
    }
  }
}