{
  "id": "2412.04561",
  "version": "v1",
  "published": "2024-12-05T19:04:44.000Z",
  "updated": "2024-12-05T19:04:44.000Z",
  "title": "Differential operators, anisotropy, and simplicial spheres",
  "authors": [
    "Kalle Karu",
    "Matt Larson",
    "Alan Stapledon"
  ],
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These identities generalize the characteristic 2 identities used by Papadakis and Petrotou to give a proof of the algebraic g-conjecture. We use these identities to prove the anisotropy of certain forms on the generic artinian reduction of the Stanley-Reisner ring and to prove weak Lefschetz results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-05T19:04:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F55",
      "05E45"
    ],
    "keywords": [
      "differential operators",
      "simplicial sphere",
      "generic artinian reduction",
      "anisotropy",
      "identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}