{
  "id": "2210.07635",
  "version": "v1",
  "published": "2022-10-14T08:31:42.000Z",
  "updated": "2022-10-14T08:31:42.000Z",
  "title": "Gauge fields on $B$-branes over $\\mathbb{CP}^n$",
  "authors": [
    "Andrés Viña"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Considering the $B$-branes over the complex projective space ${\\mathbb P}^n$ as the objects of the bounded derived category $D^b({\\mathbb P}^n)$, we prove that the cardinal of the set of holomorphic gauge fields on a given $B$-brane ${\\mathscr G}^{\\bullet}$ is $\\leq 1$. Moreover, the cardinal is $1$ iff each ${\\mathscr G}^p$ is isomorphic to a direct sum of copies of ${\\mathscr O}_{{\\mathbb P}^n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-14T08:31:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C05",
      "18G10"
    ],
    "keywords": [
      "holomorphic gauge fields",
      "direct sum",
      "complex projective space",
      "bounded derived category",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}