{
  "abstract": "Let $C$ be a smooth projective complex curve of genus $g$ and gonality $k$, and $L$ be a very ample line bundle on $C$. When $L$ has sufficiently large degree, the vanishing and nonvanishing of the Koszul cohomology groups $K_{p,q}(C,L)$ have been determined previously, but the exact values of the graded Betti numbers $κ_{p,q}(C, L)$ remain largely unknown. In this paper, we give explicit closed formulas for all graded Betti numbers $κ_{p,q}(C, L)$ when the Brill--Noether locus $W_k^1(C)$ has the expected dimension and $H^1(C, L \\otimes ω_C^{-1})=0$. Consequently, we determine the complete Betti table for a general curve when $°L \\geq 4g-3$ or when $°L \\geq 3g-3$ and $L$ is general. We also explicitly compute the Boij--Söderberg coefficient of the section ring $R(C, L)$ governing asymptotic purity, and show eventual monotonicity of the remaining coefficients: they decrease for hyperelliptic curves and increase under a natural generic reducedness assumption on the relevant Brill--Noether loci.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11161",
  "author_total": 3,
  "authors": [
    {
      "name": "JeongDon Lee"
    },
    {
      "name": "Li Li"
    },
    {
      "name": "Jinhyung Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1z5kypz5jxthp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11161",
  "fulltext_url": null,
  "id": "1z5kypz5jxthp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11161",
  "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": "W7212292779",
  "pdf_url": "https://arxiv.org/pdf/2609.11161",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1z5kypz5jxthp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11161",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11161"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Graded Betti numbers of general curves of large degree",
  "title_text": "Graded Betti numbers of general curves of large degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/1z5kypz5jxthp",
  "venue": "arXiv",
  "versions": []
}