Collineätion

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 .

Proof of collineation

It follows from

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

Properties

Consider the projective space .

  1. Automorphic collineätion criterion (fixes basis elements)

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