{
  "abstract": "Let $X_σ$ be the affine normal toric variety associated with a full-dimensional strongly convex rational polyhedral cone $σ$, and let $m$ be a primitive degree with slice $P_m=σ\\cap[m=1]$. We construct an explicit flat algebraic family whose completion is universal for equivariant deformations in all degrees $-jm$, $j\\ge1$, simultaneously. We prove that the irreducible components of the reduced base correspond bijectively to maximal lattice-friendly Minkowski decompositions of $P_m$, and describe the induced family on each component. When $m\\inσ^\\vee$, we also obtain a formally universal equivariant family for the pair $(X_σ,V(χ^m))$. These results extend earlier miniversality and component theorems to arbitrary affine normal toric varieties and arbitrary primitive degrees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10230",
  "author_total": 1,
  "authors": [
    {
      "name": "Matej Filip"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5zxcdbvhpjaw9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10230",
  "fulltext_url": null,
  "id": "5zxcdbvhpjaw9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10230",
  "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": "W7220902397",
  "pdf_url": "https://arxiv.org/pdf/2610.10230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5zxcdbvhpjaw9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10230"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Minkowski decompositions and universal equivariant deformations of toric pairs",
  "title_text": "Minkowski decompositions and universal equivariant deformations of toric pairs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/5zxcdbvhpjaw9",
  "venue": "arXiv",
  "versions": []
}