{
  "id": "math/0605758",
  "version": "v1",
  "published": "2006-05-30T13:48:20.000Z",
  "updated": "2006-05-30T13:48:20.000Z",
  "title": "Special Linear Series and Syzygies of Canonical Curves of Genus 9",
  "authors": [
    "Michael Sagraloff"
  ],
  "comment": "PhD Thesis, extended version",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this thesis we give a complete description of the syzygies of irreducible, nonsingular, canoncial curves $C$ of genus 9. This includes a collection of all possible Betti tables for $C$. Moreover a direct correspondence between these Betti tables and the number and types of special linear series on $C$ is given. Especially for $\\operatorname{Cliff}(C)=3$ the curve $C$ is contained in determinantal surface $Y$ on a 4-dimensional rational normal scroll $X\\subset \\mathbb{P}^8$ constructed from a base point free pencil of divisors of degree 5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-30T13:48:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H51"
    ],
    "keywords": [
      "special linear series",
      "canonical curves",
      "betti tables",
      "base point free pencil",
      "rational normal scroll"
    ],
    "tags": [
      "dissertation"
    ],
    "publication": {
      "journal": "Ph.D. Thesis",
      "year": 2006,
      "month": "May"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006PhDT.......405S"
    }
  }
}