{
  "id": "2402.04512",
  "version": "v1",
  "published": "2024-02-07T01:37:18.000Z",
  "updated": "2024-02-07T01:37:18.000Z",
  "title": "Multiplicative Thom-Sebastiani for Bernstein-Sato polynomials",
  "authors": [
    "Jonghyun Lee"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that if $f\\in \\mathcal{O}_X(X)$ and $g\\in \\mathcal{O}_Y(Y)$ are nonzero regular functions on smooth complex algebraic varieties $X$ and $Y$, then the Bernstein-Sato polynomial of the product function $fg \\in \\mathcal{O}_{X\\times Y}(X \\times Y)$ is given by $b_{fg}(s)=b_f(s)b_g(s)$. This answers a question of Mihnea Popa from his course notes \\cite{Pop21} on $D$-modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-07T01:37:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F10"
    ],
    "keywords": [
      "bernstein-sato polynomial",
      "multiplicative thom-sebastiani",
      "smooth complex algebraic varieties",
      "nonzero regular functions",
      "product function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}