{
  "annotation_id": "6fc17757-df06-44ec-9573-11c3847a23dd",
  "date_created": "2026-02-17T05:53:24.101000Z",
  "date_modified": "2026-02-17T05:53:24.101000Z",
  "file_hash": "0e2caea7c0eaf78f2105fc796a8d302443b1af337e9f7dbda24b4572f43af788",
  "private": false,
  "record": {
    "abstract": "We study prime Fano threefolds of genus 12 ($V_{22}$-varieties) with positive-dimensional automorphism groups in positive and mixed characteristic. We classify such varieties over any perfect field. In particular, we prove that $V_{22}$-varieties of Mukai-Umemura type over $k$ exist if and only if $\\mathrm{char}\\ k \\neq 2$, $5$. We also prove the same result for $\\mathbb{G}_a$-type. As arithmetic applications, we show that the Shafarevich conjecture holds for $V_{22}$-varieties of Mukai-Umemura type and of $\\mathbb{G}_m$-type, while it fails for $V_{22}$-varieties of $\\mathbb{G}_a$-type. Moreover, we prove that there exists $V_{22}$-varieties over $\\mathbb{Z}$, whereas there do not exist $V_{22}$-varieties over $\\mathbb{Z}$ whose generic fiber has a positive-dimensional automorphism group.",
    "arxiv_id": "2601.10106",
    "authors": [
      "Tetsushi Ito",
      "Akihiro Kanemitsu",
      "Teppei Takamatsu",
      "Yuuji Tanaka"
    ],
    "categories": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Fano threefolds of genus 12 with large automorphism group in positive and mixed characteristic",
    "url": "https://arxiv.org/abs/2601.10106",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2fa08e6e-0677-447b-aaea-6eb8bd29ce24",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}