{
  "id": "2008.11255",
  "version": "v1",
  "published": "2020-08-25T20:18:07.000Z",
  "updated": "2020-08-25T20:18:07.000Z",
  "title": "Some Remarks on H-stability of syzygy bundle on algebraic surface",
  "authors": [
    "H. Torres-López",
    "A. G. Zamora"
  ],
  "comment": "9 Pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $L$ be a globally generated line bundle over a smooth irreducible projective surface$X$. The syzygy bundle $M_{L}$ is the kernel of the evaluation map $H^0(L)\\otimes\\mathcal O_X\\to L$. The main theorem proves that the syzygy bundle defined by $nL+D$ is stable for any polarization $H$, where $L$ is any ample , $D$ is an arbitrary divisor and $n$ is a sufficiently large natural number. Taking $n=1$, we obtain the $L$-stability of $M_L$ for Hirzebruch surfaces, del Pezzo surfaces and Enriques surfaces. Finally, the $-K$-stability of syzygy bundles $M_L$ over del Pezzo surfaces is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-25T20:18:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "14J26"
    ],
    "keywords": [
      "syzygy bundle",
      "algebraic surface",
      "del pezzo surfaces",
      "h-stability",
      "sufficiently large natural number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}