nLab projective involution

Idea

A projective involution is a projective morphism from a projective space to itself which is also an involution, that is, it squares to the identity map.

For a line and a conic

An involution of a projective line is a projective involution if it preserves the cross ratio.

According to Jakob Steiner, conic may be defined as the set of intersection points of two projectively but not perspectively equivalent pencils of lines with different centers. Thus the cross ratio may be considered for a conic and a projective involution of a conic may be defined as an involution preserving the cross ratio.

Properties

See also Pappus' involution theorem.

category: geometry