{
  "id": "1711.03764",
  "version": "v1",
  "published": "2017-11-10T10:40:14.000Z",
  "updated": "2017-11-10T10:40:14.000Z",
  "title": "Positivity of line bundles on general blow-ups of abelian surfaces",
  "authors": [
    "Sanghyeon Lee",
    "Jaesun Shin"
  ],
  "comment": "17 pages, Comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $(S,L_{S})$ be a polarized abelian surface, and let $M = c \\cdot \\pi^*L_S - \\alpha \\cdot \\sum_{i=1}^r E_i$ be a line bundle on ${\\rm Bl}_{r}(S)$, where $\\pi:{\\rm Bl}_{r}(S) \\rightarrow S$ is the blow-up of $S$ at $r$ general points with exceptional divisors $E_{1},\\dots,E_{r}$. In this paper, we provide a criterion for $k$-very ampleness of $M$. Also, we deal with the case when $S$ is an arbitrary surface of Picard number one with a numerically trivial canonical divisor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-10T10:40:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14E25",
      "14K99",
      "14J25"
    ],
    "keywords": [
      "line bundle",
      "general blow-ups",
      "positivity",
      "general points",
      "numerically trivial canonical divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}