{
  "abstract": "Motivated by extending the Morrison-Kawamata cone conjecture beyond Calabi-Yau varieties and Severi-Maehara type finiteness results to targets not necessarily of general type, we fix a smooth projective variety and study the finiteness of its log canonical models as klt boundaries vary. Our main result establishes finiteness for every smooth projective minimal surface. For each $κ\\in\\{-\\infty,0,1\\}$, we construct a smooth projective non-minimal surface of Kodaira dimension $κ$ with infinitely many log canonical models, showing that the minimality assumption cannot be omitted in general. We also investigate possible extensions of this finiteness result to higher dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03305",
  "author_total": 2,
  "authors": [
    {
      "name": "Xingying Li"
    },
    {
      "name": "Zhan Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/550t170bn46m9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03305",
  "fulltext_url": null,
  "id": "550t170bn46m9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03305",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7208745657",
  "pdf_url": "https://arxiv.org/pdf/2609.03305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/550t170bn46m9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.03305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Log canonical models of a fixed variety with varying boundaries",
  "title_text": "Log canonical models of a fixed variety with varying boundaries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/550t170bn46m9",
  "venue": "arXiv",
  "versions": []
}