{
  "id": "2401.03586",
  "version": "v1",
  "published": "2024-01-07T21:44:30.000Z",
  "updated": "2024-01-07T21:44:30.000Z",
  "title": "Stability of Kernel Bundles",
  "authors": [
    "Chen Song"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we study the stability of general kernel bundles on $\\mathbb{P}^n$. Let $a,b,d>0$ be integers. A kernel bundle $E_{a,b}$ on $\\mathbb{P}^n$ is defined as the kernel of a surjective map $\\phi:\\mathcal{O}_{\\mathbb{P}^n}(-d)^a\\rightarrow \\mathcal{O}_{\\mathbb{P}^n}^b$. Here $\\phi$ is represented by a $b\\times a$ matrix $(f_{ij})$ where the entries $f_{ij}$ are polynomials of degree $d$. We give sufficient conditions for semistability of a general kernel bundle on $\\mathbb{P}^n$, in terms of its Chern class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-07T21:44:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general kernel bundle",
      "sufficient conditions",
      "surjective map",
      "polynomials",
      "semistability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}