{
  "abstract": "Let $S$ be a smooth complex projective surface endowed with a fibration $f \\colon S \\to C$ onto a smooth projective curve $C$. We prove that, if $S$ is a Mori dream space (or, more generally, if its pseudo-effective cone is polyhedral) then the Picard number $ρ(S)$ can be effectively computed by counting the irreducible components of the reducible fibres of $f$. A first simple consequence is that, given an elliptic fibration $f \\colon S \\to \\mathbb{P}^1$ with a section and such that $S$ is a Mori dream space, the Mordell-Weil group of the general fibre of $f$ is finite. The main application is a simple criterion for proving that a surface fibred over a curve is not a Mori dream space. We show that certain Horikawa surfaces, Fermat surfaces in $\\mathbb{P}^{3}$ of every degree $\\ge 4$, particular product-quotient surfaces, and the minimal simply connected numerical Godeaux surface constructed by Craighero and Gattazzo are not Mori dream spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29485",
  "author_total": 3,
  "authors": [
    {
      "name": "Federico Fallucca"
    },
    {
      "name": "Roberto Pignatelli"
    },
    {
      "name": "Francesco Polizzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9katzp490vnbd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29485",
  "fulltext_url": null,
  "id": "9katzp490vnbd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29485",
  "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": "W7204887217",
  "pdf_url": "https://arxiv.org/pdf/2608.29485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9katzp490vnbd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2608.29485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Picard number of fibred Mori dream surfaces",
  "title_text": "The Picard number of fibred Mori dream surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9katzp490vnbd",
  "venue": "arXiv",
  "versions": []
}