{
  "id": "2007.04164",
  "version": "v1",
  "published": "2020-07-08T14:51:28.000Z",
  "updated": "2020-07-08T14:51:28.000Z",
  "title": "H-instanton bundles on three-dimensional polarized projective varieties",
  "authors": [
    "Vincenzo Antonelli",
    "Francesco Malaspina"
  ],
  "comment": "27 pages. Comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We propose a notion of instanton bundle (called $H$-instanton bundle) on any projective variety of dimension three polarized by a very ample divisor $H$, that naturally generalizes the ones on $\\mathbb{P}^3$ and on the flag threefold $F(0,1,2)$. We discuss the cases of Veronese, Fano and complete intersection Calabi-Yau threefolds. Then we deal with $H$-instanton bundles $\\mathcal{E}$ on three-dimensional rational normal scrolls $S(a_0,a_1,a_2)$. We give a monadic description of $H$-instanton bundles and we prove the existence of $\\mu$-stable $H$-instanton bundles on $S(a_0,a_1,a_2)$ for any admissible charge $k=c_2(\\mathcal{E})H$. Then we deal in more detail with $S(a,a,b)$ and $S(a_0,a_1,a_2)$ with $a_0+a_1>a_2$ and even degree. Finally we describe a nice component of the moduli space of $\\mu$-stable bundles whose points represent $H$-instantons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-08T14:51:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "13C14",
      "14F05"
    ],
    "keywords": [
      "projective variety",
      "three-dimensional polarized projective varieties",
      "h-instanton bundles",
      "three-dimensional rational normal scrolls",
      "complete intersection calabi-yau threefolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}