{
  "id": "2307.05022",
  "version": "v1",
  "published": "2023-07-11T05:51:57.000Z",
  "updated": "2023-07-11T05:51:57.000Z",
  "title": "Positivity of extensions of vector bundles",
  "authors": [
    "Sho Ejiri",
    "Osamu Fujino",
    "Masataka Iwai"
  ],
  "comment": "7 pages, comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we prove that an extension of an ample line bundle by a big line bundle is not necessarily pseudo-effective. In particular, this implies that an almost nef vector bundle is not necessarily pseudo-effective. We also show that an extension of a big (resp. pseudo-effective) line bundle by an ample (resp. a nef) vector bundle is big (resp. pseudo-effective).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-11T05:51:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "14E99",
      "14F06"
    ],
    "keywords": [
      "positivity",
      "ample line bundle",
      "nef vector bundle",
      "big line bundle",
      "necessarily pseudo-effective"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}