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In this paper we consider a family of projective embeddings of the geometry$\Gamma = A_{n,\{1,n\}}(F)$ of point-hyperplanes flags of the projectivegeometry $\Sigma = PG(n,F)$. The natural embedding $\varepsilon_{mathrm{nat}}$is one of them. It maps every point-hyperplane flag $(p,H)$ of $\Sigma$ ontothe vector-line $\langle x\otimes\xi\rangle$, where $x$ is a representativevector of $p$ and $\xi$ is a linear functional describing $H$. The otherembeddings have been discovered by Thas and Van Maldeghem (2000) for the case$n = 2$ and later generalized to any $n$ by De Schepper, Schillewaert and VanMaldeghem (2023). They are obtained as twistings of$\varepsilon_{\mathrm{nat}}$ by non-trivial automorphisms of $F$. Explicitly,for $\sigma\in Aut(F)\setminus\{\mathrm{id}_F\}$, the twisting$\varepsilon_\sigma$ of $\varepsilon_{\mathrm{nat}}$ by $\sigma$ maps $(p,H)$onto $\langle x\sigma\otimes \xi\rangle$. We shall prove that, when $|Aut(F)| >1$ a geometric hyperplane $\cal H$ of $\Gamma$ arises from$\varepsilon_{\mathrm{nat}}$ and one of its twistings or from two distincttwistings of $\varepsilon_{\mathrm{nat}}$ if and only if ${\cal H} = \{(p,H)\in\Gamma \mid p\in A \mbox{ or } a \in H\}$ for a possibly non-incidentpoint-hyperplane pair $(a,A)$ of $\Sigma$. We call these hyperplanesquasi-singular hyperplanes. With the help of this result we shall prove that if$|Aut(F)| > 1$ then $\Gamma$ admits no absolutely universal embedding.

Embeddings and hyperplanes of the Lie incidence geometry $A_{n,\{1,n\}}(\mathbb{F})