{
  "id": "2101.09955",
  "version": "v1",
  "published": "2021-01-25T08:49:47.000Z",
  "updated": "2021-01-25T08:49:47.000Z",
  "title": "Algebraic differential equations of periods integrals",
  "authors": [
    "Daniel Barlet"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1512.07062",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We explain that in the study of the asymptotic expansion at the origin of a period integral like $\\gamma$z $\\omega$/df or of a hermitian period like f =s $\\rho$.$\\omega$/df $\\land$ $\\omega$ /df the computation of the Bernstein polynomial of the \"fresco\" (filtered differential equation) associated to the pair of germs (f, $\\omega$) gives a better control than the computation of the Bernstein polynomial of the full Brieskorn module of the germ of f at the origin. Moreover, it is easier to compute as it has a better functoriality and smaller degree. We illustrate this in the case where f $\\in$ C[x 0 ,. .. , x n ] has n + 2 monomials and is not quasi-homogeneous, by giving an explicite simple algorithm to produce a multiple of the Bernstein polynomial when $\\omega$ is a monomial holomorphic volume form. Several concrete examples are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-25T08:49:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic differential equations",
      "periods integrals",
      "bernstein polynomial",
      "monomial holomorphic volume form",
      "full brieskorn module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}