{
  "abstract": "We prove a Frobenius-dilation inequality for Hilbert functions of ideals generated by powers of fixed homogeneous forms in characteristic zero. Via Emsalem--Iarrobino inverse system duality, it yields quantitative fat-point postulation estimates and a new proof of the recent theorem of Ha--Sivakumar resolving Demailly's conjecture for arbitrary finite point sets. A fixed-characteristic version controls tangent spaces to varieties of powers and, together with plane interpolation and secant-theoretic results, proves complete nondefectivity of $V^k_{2,d}$ for all $k\\ge3$ and $d\\ge2$; in particular, it settles the ternary Waring problem for generic $k$-rank conjectured by Lundqvist--Oneto--Reznick--Shapiro (suggested by Ottaviani). We also show that, for a prime power exponent $q$, any failure of Nicklasson's conjecture in three variables is confined to $2q-2$ consecutive degrees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06767",
  "author_total": 2,
  "authors": [
    {
      "name": "Trung Hoa Dinh"
    },
    {
      "name": "Tai Huy Ha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/066nb61s4ybb0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06767",
  "fulltext_url": null,
  "id": "066nb61s4ybb0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06767",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7212043049",
  "pdf_url": "https://arxiv.org/pdf/2609.06767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/066nb61s4ybb0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06767"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Frobenius dilation of Hilbert function, Demailly's conjecture, and varieties of powers",
  "title_text": "Frobenius dilation of Hilbert function, Demailly's conjecture, and varieties of powers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/066nb61s4ybb0",
  "venue": "arXiv",
  "versions": []
}