Year: 2026
Type: preprint
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 $PGL_{n+1}(F)$ on the projective space $\mathbb{P}^n(F)$. More precisely, we establish the Borovik-Cherlin conjecture for permutation groups $(G,X)$ definable in models of $ACF$.
Source: arXiv (Cornell University)
Authors: Karhumäki, Ulla, Ramsey, Nicholas
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207668762