{
  "id": "1906.05859",
  "version": "v1",
  "published": "2019-06-14T14:16:20.000Z",
  "updated": "2019-06-14T14:16:20.000Z",
  "title": "FAQ on the g-theorem and the hard Lefschetz theorem for face rings",
  "authors": [
    "Karim Adiprasito"
  ],
  "comment": "Review article, 12 pages",
  "categories": [
    "math.CO",
    "math.AC",
    "math.AG",
    "math.GT"
  ],
  "abstract": "This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the $g$-theorem. We give a review over the two available proofs of the hard Lefschetz theorem for simplicial spheres, as well as recent work of Karu, Steinmeyer and the author, all of which share a common core introduced in arxiv:1812.10454: perturbations of maps, biased Poincar\\'e pairings and a cobordism argument that relates the Lefschetz property of a manifold to the Lefschetz property on its boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-14T14:16:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hard lefschetz theorem",
      "face rings",
      "lefschetz property",
      "author gave",
      "short review"
    ],
    "tags": [
      "review article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}