{
  "abstract": "Let B be a plane curve which has simple normal crossings. We prove that, if B = B_1 \\cup B_2 has two irreducible components with deg B_1, deg B_2 \\geq 5 or deg B_1 = 4, deg B_2 \\geq 7, and if B is general, then the associated algebraic exceptional set is empty. Based on this, we show that for a general plane curve B satisfying \\bar{c}_1^2 - \\bar{c}_2 > 0, the open surface \\mathbb{P}^2 \\setminus B is Kobayashi hyperbolic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37777",
  "author_total": 1,
  "authors": [
    {
      "name": "Wei Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5032exb1m1cpw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37777",
  "fulltext_url": null,
  "id": "5032exb1m1cpw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37777",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214959058",
  "pdf_url": "https://arxiv.org/pdf/2609.37777",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5032exb1m1cpw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37777",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37777"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exceptional Loci and Hyperbolicity of Complements of Plane Curves with $\\bar{c}_1^2 - \\bar{c}_2 > 0$",
  "title_text": "Exceptional Loci and Hyperbolicity of Complements of Plane Curves with c̅_1^2 − c̅_2 > 0",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/5032exb1m1cpw",
  "venue": "arXiv",
  "versions": []
}