{
  "abstract": "We introduce the analogue, for invariant jet differentials, of the principal symbol of a differential operator: the component of maximal degree in the highest derivative. The top symbol identifies a canonical quotient bundle of the Demailly--Semple bundle $E_{k,m}T^*_X$, with values in jet differentials of lower order, and together with the Brückmann--Rackwitz vanishing theorem it gives a non-ampleness criterion for $E_{k,m}T^*_Z$ on complete intersections $Z\\subset\\PP^N$. On the Demailly--Semple tower the top symbol is the restriction to a thickening of the vertical divisor, inside the singular jets. The criterion applies in orders $3$ and $4$: $E_{3,5q}T^*_X$ is not ample on any smooth hypersurface $X\\subset\\PP^4$, and $E_{4,m}T^*_X$ is not ample for $m\\ge7$ with $m\\equiv0,1,2\\pmod 7$ on any smooth hypersurface $X\\subset\\PP^5$ of degree at least $2$. This contradicts the Diverio--Trapani conjecture at its own threshold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33710",
  "author_total": 1,
  "authors": [
    {
      "name": "Simone Diverio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frvdcykywwnxz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33710",
  "fulltext_url": null,
  "id": "frvdcykywwnxz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33710",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214721683",
  "pdf_url": "https://arxiv.org/pdf/2609.33710",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frvdcykywwnxz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2609.33710",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33710"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Obstructions to the ampleness of invariant jet differentials on complete intersections",
  "title_text": "Obstructions to the ampleness of invariant jet differentials on complete intersections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/frvdcykywwnxz",
  "venue": "arXiv",
  "versions": []
}