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PreprintarXiv licencearXiv

The Borovik-Cherlin conjecture holds in ACF

  • Ulla Karhumäki
  • Nicholas Ramsey
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Abstract

We show that every faithful, transitive, and generically (n+2)-transitive action of a connected group G on an irreducible variety X of dimension n > 0, all defined over an algebraically closed field F, is isomorphic to the natural action of the projective linear group PGLn+1(F) on the projective space ℙn(F). More precisely, we establish the Borovik-Cherlin conjecture for permutation groups (G,X) definable in models of ACF.

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Cite

BibTeXRIS
BibTeX
@misc{karhumaki2026borovikcherlin,
  title = {{The Borovik-Cherlin conjecture holds in ACF}},
  author = {Ulla Karhumäki and Nicholas Ramsey},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02198},
  eprint = {2609.02198},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02198},
}
RIS
TY  - UNPB
TI  - The Borovik-Cherlin conjecture holds in ACF
AU  - Ulla Karhumäki
AU  - Nicholas Ramsey
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02198
UR  - https://arxiv.org/abs/2609.02198
AB  - We show that every faithful, transitive, and generically (n+2)-transitive action of a connected group G on an irreducible variety X of dimension n > 0, all defined over an algebraically closed field F, is isomorphic to the natural action of the projective linear group PGL_n+1(F) on the projective space ℙ^n(F). More precisely, we establish the Borovik-Cherlin conjecture for permutation groups (G,X) definable in models of ACF.
ER  -