{
  "id": "2210.14781",
  "version": "v1",
  "published": "2022-10-26T15:20:51.000Z",
  "updated": "2022-10-26T15:20:51.000Z",
  "title": "On K-moduli of quartic threefolds",
  "authors": [
    "Hamid Abban",
    "Ivan Cheltsov",
    "Alexander Kasprzyk",
    "Andrea Petracci"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "The family of smooth Fano 3-folds with Picard rank 1 and anticanonical volume 4 consists of quartic 3-folds and of double covers of the 3-dimensional quadric branched along an octic surface; all of them are K-stable. With the aim of investigating the compactification of the moduli space of quartic 3-folds given by K-stability, we exhibit K-polystable Fano 3-folds which deform to quartic 3-folds, but which are neither quartic 3-folds nor double covers of quadric 3-folds. The examples we find are complete intersections of two quadrics and a quartic in the weighted projective space $\\mathbb{P}(1,1,1,1,1,2,2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-26T15:20:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "32Q20"
    ],
    "keywords": [
      "quartic threefolds",
      "double covers",
      "complete intersections",
      "smooth fano",
      "picard rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}