{
  "abstract": "Explicit computations of generic infinitesimal Newton--Okounkov bodies are difficult even for varieties with simple product structure. We give an explicit formula in arbitrary dimension for positive-degree external tensor products on products of smooth projective curves. Writing $d^\\downarrow=(d_1^\\downarrow,\\ldots,d_n^\\downarrow)$ for the decreasing rearrangement of the degree vector and setting $d_{n+1}^\\downarrow=0$, the body admits the explicit Minkowski decomposition $\\sum_{j=1}^n(d_j^\\downarrow-d_{j+1}^\\downarrow)S_j^{(n)}$, where the $S_j^{(n)}$ are the embedded simplices defined below. Using this description, we give a sharp criterion for equality in the Minkowski inclusion. A simultaneous relabeling argument also allows finitely many such bodies to be realized on a common very general locus of flags after independent decreasing rearrangements of their degree vectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17469",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/anadj07vqd7v8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17469",
  "fulltext_url": null,
  "id": "anadj07vqd7v8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17469",
  "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": "W7213416855",
  "pdf_url": "https://arxiv.org/pdf/2609.17469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/anadj07vqd7v8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves",
  "title_text": "Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/anadj07vqd7v8",
  "venue": "arXiv",
  "versions": []
}