Dualities and polarities

A duality of a projective plane is just an isomorphism of onto the dual projective plane .

A duality is called a polarity if and for all points p and lines l of , respectively.

Important examples of polarities arise from bilinear forms. Given a three-dimensional vector space V over a skew field K, and a non-degenerate hermitean, sesquilinear form , the map defined by

defines a polarity of the projective plane over V.

An absolute point p of a polarity is a point p of with . Absolute lines are defined similarly.

Contributed by Hauke Klein
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