Automorphic collineation

An automorphic collineätion is a Collineätion of a projective space given by a field automorphism applied coördinatewise, #m/def/geo hence it is the action of $A u t (𝕂)$ .

Proof of collineation

It follows from

(𝑛 \sum 𝑖 = 0 𝜆 𝑖 𝐱 𝑖) 𝜎 = 𝑛 \sum 𝑖 = 0 𝜆 𝜎 𝑖 𝐱 𝜎 𝑖

that $𝑑$ -dimensional linear subspaces are mapped to $𝑑$ -dimensional linear subspaces and containment/incidence is preserved. Hence $𝜎$ induces a collineation.

Properties

Consider the projective space $P G (𝑛, 𝕂)$ .

Automorphic collineätion criterion (fixes basis elements)

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