Projective Varieties

Abstract

Projective Geometry, as described in [20] by Hilbert and Cohn-Vossen, is a study of “geometrical facts that can be formulated and proved without any measurement or comparison of distances and angles”. To quote their example:

⋯ if a plane figure is projected from a point onto another plane, distances and angles are changed, and in addition, parallel lines may be changed into lines that are not parallel; but certain essential properties must nevertheless remain intact, since we could not otherwise recognise the projection as being a true picture of the original figure.