{
  "abstract": "In this article, we study how the absolute coregularity of a projective log pair reflects on its fundamental group. More precisely, we show that for a projective klt log pair $(X,D)$ of absolute coregularity $c$ and arbitrary dimension the fundamental group $π_1^{\\rm reg}(X,D)$ admits a normal abelian subgroup of finite index and rank at most $2c$. We reduce this statement to klt Calabi-Yau pairs with standard coefficients of dimension $c$. In the cases $0\\le c\\le2$ and fixed dimension, we can furthermore bound the index of a solvable normal subgroup. Combining the reduction with the recent regular-locus theorem of Fu-Guo-Song-Wang, we prove the coregularity bound in every dimension. In particular, for a projective klt pair $(X,D)$ with $-(K_X+D)$ nef, the orbifold fundamental group of the smooth locus is virtually abelian of rank at most $2\\, {\\rm dim}X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21358",
  "author_total": 2,
  "authors": [
    {
      "name": "Lukas Braun"
    },
    {
      "name": "Fernando Figueroa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/084pjyrg5dacx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21358",
  "fulltext_url": null,
  "id": "084pjyrg5dacx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21358",
  "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": "W7222537079",
  "pdf_url": "https://arxiv.org/pdf/2610.21358",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/084pjyrg5dacx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21358",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21358"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fundamental Groups and Coregularity: Klt Pairs with Trivial and Nef Log-Anticanonical Class",
  "title_text": "Fundamental Groups and Coregularity: Klt Pairs with Trivial and Nef Log-Anticanonical Class",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/084pjyrg5dacx",
  "venue": "arXiv",
  "versions": []
}