{
  "abstract": "We construct a smooth projective family of rational surfaces over $\\mathbb{G}_{m,\\mathbb{Z}}$. The Mori dream property of a fiber is determined by the torsion of the normal bundle of an anticanonical cycle. Over $\\mathbb{C}$, the locus of Mori dream fibers is Zariski dense. For every prime $p$, every geometric fiber over a closed point of the reduction modulo $p$ is a Mori dream surface, whereas the geometric generic fiber is not a Mori dream space. In either setting, no restriction to a nonempty open subset is a Mori dream morphism. We also prove that, over any algebraically closed field, a projective fibration becomes a Mori dream morphism after shrinking the base whenever the set of points with Mori dream fibers is not contained in a countable union of proper closed subsets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17103",
  "author_total": 2,
  "authors": [
    {
      "name": "Dae-Won Lee"
    },
    {
      "name": "Masaru Nagaoka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/asv2snhny7mx8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17103",
  "fulltext_url": null,
  "id": "asv2snhny7mx8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17103",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213436672",
  "pdf_url": "https://arxiv.org/pdf/2609.17103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/asv2snhny7mx8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Mori dream fibers and the geometric generic fiber",
  "title_text": "Mori dream fibers and the geometric generic fiber",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/asv2snhny7mx8",
  "venue": "arXiv",
  "versions": []
}