{
  "abstract": "Let $X$ be a nonsingular complex projective surface and let $L$ be a very ample line bundle on $X$. We study the question: when does a general pencil in the linear system $|L|$ consist of only irreducible and reduced curves? We give a precise condition which guarantees an affirmative answer: in fact, this holds if and only if the genus of a general member of $|L|$ exceeds the irregularity of $X$. The proof is topological, using vanishing cycles and the theory of Lefschetz pencils. As an application, combined with a construction due to Miranda, we prove that for any positive rational number $δ$ there exist a blow up $Y \\to X$ at finitely many points, an ample line bundle $M$ on $Y$ and a point $x \\in Y$ such that $\\varepsilon(Y,M,x) = δ$; Miranda proved this when $X = \\mathbb{P}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23485",
  "author_total": 2,
  "authors": [
    {
      "name": "Krishna Hanumanthu"
    },
    {
      "name": "A. J. Parameswaran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2gaynkrxkq7y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23485",
  "fulltext_url": null,
  "id": "b2gaynkrxkq7y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23485",
  "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": "W7222954005",
  "pdf_url": "https://arxiv.org/pdf/2610.23485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2gaynkrxkq7y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lefschetz Pencils on surfaces and an application to Seshadri constants",
  "title_text": "Lefschetz Pencils on surfaces and an application to Seshadri constants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/b2gaynkrxkq7y",
  "venue": "arXiv",
  "versions": []
}