{
  "id": "2201.13251",
  "version": "v1",
  "published": "2022-01-31T14:00:06.000Z",
  "updated": "2022-01-31T14:00:06.000Z",
  "title": "Stability conditions on fibred threefolds",
  "authors": [
    "Hao Max Sun"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We give a conjectural construction of Bridgeland stability conditions on the derived category of fibred threefolds. The construction depends on a conjectural Bogomolov-Gieseker type inequality for certain stable complexes. It can be considered as a relative version of the construction of Bayer, Macr\\`i and Toda. We prove the conjectural Bogomolov-Gieseker type inequalities in the case of relative projective planes over curves. This gives the the existence of Bridgeland stability conditions on such threefolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-31T14:00:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fibred threefolds",
      "conjectural bogomolov-gieseker type inequality",
      "bridgeland stability conditions",
      "conjectural construction",
      "stable complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}