{
  "id": "2207.01096",
  "version": "v1",
  "published": "2022-07-03T18:45:07.000Z",
  "updated": "2022-07-03T18:45:07.000Z",
  "title": "Balanced rational curves and rigid curves of all genera on some Calabi-Yau complete intersections",
  "authors": [
    "Ziv Ran"
  ],
  "categories": [
    "math.AG",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "Let $X$ be either a general hypersurface of degree $n+1$ in $\\mathbb P^n$ or a general $(2,n)$ complete intersection in $\\mathbb P^{n+1}, n\\geq 4$. We construct balanced rational curves on $X$ of all high enough even degrees. If $n=3$ or $g=1$, we construct rigid curves of genus $g$ on $X$ of all high enough even degrees. As an application we construct some rigid bundles on Calabi-Yau threefolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-03T18:45:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calabi-yau complete intersections",
      "construct rigid curves",
      "construct balanced rational curves",
      "general hypersurface",
      "rigid bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}