{
  "abstract": "Let $(X,L)$ be a polarized complex abelian surface with $L^2=2d$. We establish a Reider-type criterion for Property $N_p$. If $d\\geq7$, then $L$ satisfies Property $N_0$ if and only if there is no elliptic curve $E\\subseteq X$ with $L\\cdot E\\leq2$, with one explicitly described exception. If $p\\geq1$ and $d\\geq(p+2)^2+1$, then $L$ satisfies Property $N_p$ if and only if there is no elliptic curve $E\\subseteq X$ with $L\\cdot E\\leq p+2$. The numerical bounds on $d$ are optimal for $p=0,1$. These results improve upon earlier work of Küronya--Lozovanu, Ito, and Rojas. We also construct a polarized abelian surface whose basepoint-freeness threshold is irrational.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27921",
  "author_total": 3,
  "authors": [
    {
      "name": "Chunyi Li"
    },
    {
      "name": "Lei Song"
    },
    {
      "name": "Xiao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5n4j0zpya4e4c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27921",
  "fulltext_url": null,
  "id": "5n4j0zpya4e4c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27921",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204790239",
  "pdf_url": "https://arxiv.org/pdf/2608.27921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5n4j0zpya4e4c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.27921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Syzygies of Polarized Abelian Surfaces: A Reider-Type Criterion",
  "title_text": "Syzygies of Polarized Abelian Surfaces: A Reider-Type Criterion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/5n4j0zpya4e4c",
  "venue": "arXiv",
  "versions": []
}