{
  "abstract": "We study arrangements of conics and lines in the complex projective plane from the viewpoint of 4-manifolds. We introduce combinatorial conic-line arrangements, the conic-line counterpart of rank-3 matroids, together with their topological and smooth realisations, and we ask which restrictions on a complex arrangement survive when its components are replaced by locally-flat spheres in the same homology classes with the same local singularity models. For an ADE combinatorial conic-line arrangement of even total degree admitting a topological realisation we prove a Hirzebruch-type inequality; the proof uses only branched covers and the local topology of rational double points. In the complex-algebraic category we show that equality holds exactly when the arrangement is a maximising curve, hence free with prescribed exponents. We then introduce divisible and odd combinatorial conic-line arrangements and obtain inequalities and congruences for the multiplicity sequence of their resolutions, via cyclic branched covers, the G-signature theorem, spin structures, and Furuta's 10/8-theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12192",
  "author_total": 2,
  "authors": [
    {
      "name": "Marco Golla"
    },
    {
      "name": "Piotr Pokora"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/athswy52wzvxe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12192",
  "fulltext_url": null,
  "id": "athswy52wzvxe",
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  "landing_url": "https://arxiv.org/abs/2610.12192",
  "language": "en",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
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      "arxiv",
      "math.CO"
    ],
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      "math.GT"
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      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7221176754",
  "pdf_url": "https://arxiv.org/pdf/2610.12192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/athswy52wzvxe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12192"
    },
    {
      "first_seen": "2026-10-31T12:20:56Z",
      "native_id": "hal-05845871",
      "source": "hal",
      "url": "https://hal.science/hal-05845871v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Topological inequalities for conic-line arrangements with some prescribed singularities",
  "title_text": "Topological inequalities for conic-line arrangements with some prescribed singularities",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/athswy52wzvxe",
  "venue": "arXiv",
  "versions": []
}