{
  "id": "2003.06303",
  "version": "v1",
  "published": "2020-03-13T14:02:26.000Z",
  "updated": "2020-03-13T14:02:26.000Z",
  "title": "On the families of hyperplane sections of some smooth projective varieties",
  "authors": [
    "Yong Hu"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this note, we give two applications of \\cite[Theorem 3.1]{Hwang}. We first study the free family $\\mathcal{K}$ of hyperplane sections of the smooth hypersurface $X\\subset\\mathbb{P}^{n+1}$ of degree $d\\ge 3$. We prove that $X$ is determined by the free family $\\mathcal{K}$ if $\\dim(X)\\ge 4$. As an application, we deduce that for $n\\ge 4$, the hyperplane section of $X$ varies maximally in the moduli space of the smooth hypersurface of degree $d\\ge 3$ in $\\mathbb{P}^n$. We then study the free family of hyperplane sections of the smooth projective surface $X$ with Kodaira dimension $\\kappa(X)\\ge 0$. We prove that $X$ is determined by this free family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-13T14:02:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperplane section",
      "smooth projective varieties",
      "free family",
      "smooth hypersurface",
      "kodaira dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}