{
  "id": "2307.10077",
  "version": "v1",
  "published": "2023-07-19T15:51:12.000Z",
  "updated": "2023-07-19T15:51:12.000Z",
  "title": "Monads on Cartesian products of projective spaces",
  "authors": [
    "Damian Maingi"
  ],
  "comment": "16 pages, the results proved follow the same trend with arXiv:2202.07876, arXiv:2301.04932",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we establish the existence of monads on special Cartesian products of projective spaces. Special in the sense that we mimick monads on instanton bundles. We construct monads on $\\mathbb{P}^1\\times\\cdots\\times\\mathbb{P}^1\\times\\mathbb{P}^3\\times\\cdots\\times\\mathbb{P}^3\\times\\mathbb{P}^5\\times\\cdots\\times\\mathbb{P}^5$. We proceed to prove stability of the kernel bundle associated to the monad and simplicity of the cohomology vector bundle. Specifically we establish the existence of monads on $\\mathbb{P}^{a_1}\\times\\cdots\\times\\mathbb{P}^{a_n }$ where $a_1<a_2<\\ldots<a_n$, alternating even and odd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-19T15:51:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60"
    ],
    "keywords": [
      "projective spaces",
      "special cartesian products",
      "cohomology vector bundle",
      "instanton bundles",
      "mimick monads"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}