{
  "abstract": "We prove that the relative log canonical algebra of a semi-dlt pair $(X,Δ_X)$ projective over a scheme $T$ is finitely generated, equivalently, that $(X,Δ_X)$ admits a relative stable model, provided that the normalization admits a log canonical model over $T$, that $(X,Δ_X)$ admits a stable model over an open dense subscheme $T^0\\subset T$ whose exceptional locus does not contain any stratum of the conductor, and that the log centers contained in the conductor have images meeting $T^0$. Our main contribution is a direct proof that avoids Kollár's gluing theory entirely. As a consequence, we recover demi-normal versions of results of Hacon--Xu and Birkar. Furthermore, we derive the existence of certain MMP steps for slc pairs, recovering results of Ambro and Kollár. Finally, these results lay the groundwork for a streamlined proof of the properness of the Kollár--Shepherd-Barron--Alexeev moduli space of stable pairs, to be completed in forthcoming work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36018",
  "author_total": 1,
  "authors": [
    {
      "name": "Alberto Landi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/af12861egs8qe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36018",
  "fulltext_url": null,
  "id": "af12861egs8qe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36018",
  "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": "W7214991263",
  "pdf_url": "https://arxiv.org/pdf/2609.36018",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/af12861egs8qe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36018",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36018"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite generation of relative log canonical algebras of semi-dlt pairs",
  "title_text": "Finite generation of relative log canonical algebras of semi-dlt pairs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/af12861egs8qe",
  "venue": "arXiv",
  "versions": []
}