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