{
  "id": "2405.18022",
  "version": "v1",
  "published": "2024-05-28T10:11:18.000Z",
  "updated": "2024-05-28T10:11:18.000Z",
  "title": "Syzygies of algebraic varieties through symmetric products of algebraic curves",
  "authors": [
    "Jinhyung Park"
  ],
  "comment": "22 pages, survey paper for Proceedings of MSJ-KMS Joint Meeting held in Sendai in September 2023",
  "categories": [
    "math.AG"
  ],
  "abstract": "This is a survey paper on recent work on syzygies of algebraic varieties. We discuss the gonality conjecture on weight-one syzygies of algebraic curves, syzygies of secant varieties of algebraic curves, syzygies of tangent developable surfaces and Green's conjecture on syzygies of canonical curves, and asymptotic syzygies of algebraic varieties. All results considered in this paper were proven using the geometry of symmetric products of algebraic curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-28T10:11:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic curves",
      "algebraic varieties",
      "symmetric products",
      "asymptotic syzygies",
      "gonality conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}