{
  "abstract": "The Sylvester sequence is defined recursively by $s_1=2$ and $s_i=s_{1}\\cdots s_{i-1}+1$. In this paper, we prove that the Fano index of an $n$-dimensional well-formed weighted projective space with canonical singularities is bounded above by \\[ (s_n-1)(2s_n-3). \\] This gives an affirmative answer to a conjecture of Chengxi Wang for weighted projective spaces and $\\mathbb Q$-factorial toric Fano varieties with Picard number one. We also investigate the distribution of Fano indices among $4$-dimensional weighted projective spaces. As the distribution of Fano indices of weighted projective spaces coincides with that of indices of terminal Calabi--Yau varieties in dimension $n\\leq 3$, we expect this coincidence to persist also in dimension 4, and more generally, in all dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.03434",
  "author_total": 1,
  "authors": [
    {
      "name": "Haidong Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fb6s38g86qzac.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.03434",
  "fulltext_url": null,
  "id": "fb6s38g86qzac",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.03434",
  "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": "W7172505025",
  "pdf_url": "https://arxiv.org/pdf/2608.03434",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fb6s38g86qzac.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2608.03434",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.03434"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Fano indices of weighted projective spaces",
  "title_text": "On Fano indices of weighted projective spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/fb6s38g86qzac",
  "venue": "arXiv",
  "versions": []
}