{
  "abstract": "Let $π\\colon X\\to S$ be a smooth ramified cyclic cover of an anticanonical rational surface, with $κ(X)\\geq0$, and let $A$ be a divisor on $S$. We prove a Reider-type theorem for syzygies: for every integer $p\\ge 0$, the adjoint divisor $K_X+π^*A$ satisfies Property $\\mathrm{N}_p$ provided that $A\\cdot C\\geq p+3$ for every curve $C\\subseteq S$ with $C^2\\le 1$. One ingredient is a syzygy criterion for finite covers that reduces the weight-two Koszul vanishing on $X$ to weight-one vanishing for the nontrivial character modules on $S$. The most delicate case, in which $\\dim|-K_S|=0$ and $K_S^2<0$, is handled by a separate geometric argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02000",
  "author_total": 1,
  "authors": [
    {
      "name": "Lei Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dm08sqwpnga8h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02000",
  "fulltext_url": null,
  "id": "dm08sqwpnga8h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02000",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02000",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dm08sqwpnga8h.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02000",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02000"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Reider-type theorem for syzygies of cyclic covers of anticanonical rational surfaces",
  "title_text": "A Reider-type theorem for syzygies of cyclic covers of anticanonical rational surfaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/dm08sqwpnga8h",
  "venue": "arXiv",
  "versions": []
}