{
  "abstract": "Winkelmann conjectures that every smooth flexible complex affine variety of dimension at least two is a Rosay--Rudin space. We verify this for every positive-dimensional quotient $G/H$ with $G$ a connected complex semisimple algebraic group and $H$ a closed connected reductive subgroup. Weak and strong tameness coincide, every injection between tame discrete sets extends to a holomorphic automorphism, and complements of tame, finite, or empty sets are Oka. Every sufficiently sparse enumerated sequence can be sent to a fixed sequence by a composition of $n$ complete holomorphic flow maps, with $n\\le6$; injective self-maps of the fixed sequence admit such a realization with $n\\le2$. These flows preserve an invariant algebraic volume form. The proof uses entire interpolation and regular functions invariant under two solvable subgroups to construct the automorphisms. If $G$ is simple of rank at least two and $G/H$ is spherical and admits a closed equivariant embedding into an irreducible module, the normalization bound improves to $n\\le4$. We also prove that $\\SL_2/N(T)$, where $T$ is a maximal torus, is an RR-space. This quotient is the complement of a smooth conic in $\\mathbf P^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05479",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Dvorsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dht1apw5d5j63.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05479",
  "fulltext_url": null,
  "id": "dht1apw5d5j63",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05479",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.05479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dht1apw5d5j63.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Tame Discrete Sets on Affine Semisimple Homogeneous Spaces",
  "title_text": "Tame Discrete Sets on Affine Semisimple Homogeneous Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dht1apw5d5j63",
  "venue": "arXiv",
  "versions": []
}