{
  "id": "2209.03543",
  "version": "v1",
  "published": "2022-09-08T02:54:31.000Z",
  "updated": "2022-09-08T02:54:31.000Z",
  "title": "Resolutions of local face modules, functoriality, and vanishing of local $h$-vectors",
  "authors": [
    "Matt Larson",
    "Sam Payne",
    "Alan Stapledon"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the local face modules of triangulations of simplices, i.e., the modules over face rings whose Hilbert functions are local $h$-vectors. In particular, we give resolutions of these modules by subcomplexes of Koszul complexes as well as functorial maps between modules induced by inclusions of faces. As applications, we prove a new monotonicity result for local $h$-vectors and new results on the structure of faces in triangulations with vanishing local $h$-vectors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-08T02:54:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "13F55",
      "06A07"
    ],
    "keywords": [
      "local face modules",
      "resolutions",
      "functoriality",
      "triangulations",
      "monotonicity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}