{
  "id": "1907.05180",
  "version": "v1",
  "published": "2019-07-11T13:22:29.000Z",
  "updated": "2019-07-11T13:22:29.000Z",
  "title": "Rank-1 sheaves and stable pairs on del Pezzo surfaces",
  "authors": [
    "Thomas Goller",
    "Yinbang Lin"
  ],
  "comment": "28 pages. Comments are welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study rank 1 sheaves and stable pairs on a del Pezzo surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which agrees with the usual deformation-obstruction theory. The perfect obstruction theory defines a virtual fundamental class on the moduli space. Using the embedding, we show that the virtual class equals the Euler class of a vector bundle on the smooth ambient space. As an application, we show that on $\\mathbb{P}^2$, the expected count of the finite Quot scheme in arXiv:1610.04185 is its actual length. We also obtain a universality result for tautological integrals on the moduli space of stable pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-11T13:22:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14D22"
    ],
    "keywords": [
      "del pezzo surface",
      "stable pairs",
      "moduli space",
      "perfect obstruction theory defines",
      "virtual fundamental class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}