{
  "id": "2012.12140",
  "version": "v1",
  "published": "2020-12-22T16:23:26.000Z",
  "updated": "2020-12-22T16:23:26.000Z",
  "title": "Betti structures of hypergeometric equations",
  "authors": [
    "Davide Barco",
    "Marco Hien",
    "Andreas Hohl",
    "Christian Sevenheck"
  ],
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We study Betti structures in the solution complexes of confluent hypergeometric equations. We use the framework of enhanced ind-sheaves and the irregular Riemann-Hilbert correspondence of D'Agnolo-Kashiwara. The main result is a group theoretic criterion that ensures that enhanced solutions of such systems are defined over certain subfields of the complex numbers. The proof uses a description of the hypergeometric systems as exponentially twisted Gauss-Manin systems of certain Laurent polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-22T16:23:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32C38",
      "14F10",
      "32S40"
    ],
    "keywords": [
      "irregular riemann-hilbert correspondence",
      "study betti structures",
      "group theoretic criterion",
      "confluent hypergeometric equations",
      "laurent polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}