Law of Projective Geometry

The designation main theorem of projective geometry is used in the mathematical literature for the following different theorems.

A projectivity between projective straight lines is determined when three points of one straight line and its three image points are given on the other straight line. (See Pappos' theorem .)
A projectivity between Pappus projective planes is determined when four points are given in a general position in one plane and their four image points in the other plane. (See projectivity .)
Every collineation of a projective space of dimension is a semilinear mapping. ${\ displaystyle \ geq 2}$ (See Collineation # Collineations in Projective Geometry .)
Every straight line in straight lines mapping biholomorphic mapping of two open subsets is the restriction of a projective-linear mapping. ${\ displaystyle f \ colon U \ to U ^ {\ prime}}$ ${\ displaystyle U, U ^ {\ prime} \ subset \ mathbb {C} P ^ {n \ geq 2}}$

literature

Reinhold Baer : Linear algebra and projective geometry. Academic Press Inc., New York, NY, 1952.
Emil Artin : Geometric algebra. Interscience Publishers, Inc., New York-London, 1957.