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Topological inequalities for conic-line arrangements with some prescribed singularities — arXiv:2610.12192

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.12192
License (as archived): CC0-1.0
Archived: 2026-10-09T06:29:18.808Z
SHA-256 of the archived text: efc6e75d12f61adf0553e2ba1cb357599313636a134352ab03895a8f243d05b3
Stable URL of this page: https://metraipolis.com/documento/dc_2b60fa782853

How to cite

Topological inequalities for conic-line arrangements with some prescribed singularities — arXiv:2610.12192 — arXiv (en), https://arxiv.org/abs/2610.12192 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2b60fa782853 (Metraipolis archive dc_2b60fa782853, sha256 efc6e75d12f61adf0553e2ba1cb357599313636a134352ab03895a8f243d05b3)

BibTeX

@misc{dc2b60fa782853,
  title = {Topological inequalities for conic-line arrangements with some prescribed singularities — arXiv:2610.12192},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.12192},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2b60fa782853; sha256 efc6e75d12f61adf0553e2ba1cb357599313636a134352ab03895a8f243d05b3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.12192. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Geometric Topology (math.GT) ; Algebraic Geometry (math.AG); Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.12192 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:53:57.407Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).