{
  "abstract": "We say that an affine variety $X$ is (semi)rigid if all nontrivial actions of the additive group on $X$ have the same invariant ring. Then all such actions comprise the abelian subgroup denoted $\\mathrm{SAut}(X)$. We prove that $X$ is (semi)rigid precisely when the neutral component $\\mathrm{Aut}^\\circ(X)$ of its automorphism group is nested. In this case, the neutral component is the semidirect product of any maximal algebraic torus and $\\mathrm{SAut}(X)$. The proof uses Laurent expansions of algebraic curves in $\\mathrm{Aut}^\\circ(X)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10401",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Perepechko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8x44m2z1dmq46.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10401",
  "fulltext_url": null,
  "id": "8x44m2z1dmq46",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10401",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212129576",
  "pdf_url": "https://arxiv.org/pdf/2609.10401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8x44m2z1dmq46.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:16Z",
      "native_id": "2609.10401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10401"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Neutral components of automorphism groups of (semi)rigid affine varieties",
  "title_text": "Neutral components of automorphism groups of (semi)rigid affine varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/8x44m2z1dmq46",
  "venue": "arXiv",
  "versions": []
}