{
  "id": "math/0701511",
  "version": "v1",
  "published": "2007-01-18T17:44:21.000Z",
  "updated": "2007-01-18T17:44:21.000Z",
  "title": "Examples of Calabi-Yau 3-folds of $\\mathbb{P}^7$ with $ρ=1$",
  "authors": [
    "Marie-Am\\' elie Bertin"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We give some examples of Calabi-Yau 3-folds with $\\rho=1$, defined over $\\mathbb{Q}$ and constructed as 4-codimensional subvarieties of $\\mathbb{P}^7$ via commutative algebra methods. We explain how to deduce their Hodge diamond and top Chern classes from computer based computations over some finite field $\\mathbb{F}_{p}$. Three of our examples are new. These examples are built out of Gulliksen-Neg\\r{a}rd and Kustin-Miller complexes of locally free sheaves. Finally, we give two new examples of Calabi-Yau 3-folds of $\\mathbb{P}^6$ of degree 14 and 15 that are not deformation-equivalent to the previously known examples of these degrees in $\\mathbb{P}^6$ (even though they share the same invariants $(H^3, c_2\\cdot H, c_3)$ and $\\rho=1$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-18T17:44:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "14J30",
      "14P99"
    ],
    "keywords": [
      "calabi-yau",
      "commutative algebra methods",
      "hodge diamond",
      "finite field",
      "kustin-miller complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1511B"
    }
  }
}