{
  "abstract": "Let \\(S\\) be a smooth projective complex surface with irregularity \\(q=h^{1,0}(S)\\) and geometric genus \\(g=h^{2,0}(S)\\), and let \\(S^{[n]}\\) denote its Hilbert scheme of \\(n\\) points. We prove that, for every \\(n\\ge0\\), the sequence \\[ \\left(h^{p,0}\\bigl(S^{[n]}\\bigr)\\right)_{p=0}^{2n} \\] is log-concave if and only if \\(g\\le\\binom{q+1}{2}\\). Moreover, log-concavity of all these sequences is already equivalent to log-concavity of the sequence for \\(n=2\\). We also prove that these sequences are unimodal for every \\(n\\ge0\\) if and only if \\(q\\ge1\\) or \\(g=0\\), and that this condition is already detected by the sequence for \\(n=1\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04095",
  "author_total": 1,
  "authors": [
    {
      "name": "Anubhab Pahari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2tjxem9hznv92.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04095",
  "fulltext_url": null,
  "id": "2tjxem9hznv92",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04095",
  "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"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7208779222",
  "pdf_url": "https://arxiv.org/pdf/2609.04095",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2tjxem9hznv92.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.04095",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04095"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Log-concavity and unimodality of Hodge numbers of Hilbert schemes of points over a surface",
  "title_text": "Log-concavity and unimodality of Hodge numbers of Hilbert schemes of points over a surface",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/2tjxem9hznv92",
  "venue": "arXiv",
  "versions": []
}