nLab projective geometry

Idea

Projective geometry is the study of the geometrical properties of projective spaces which are invariant under projective maps (transformations). By extension, projective geometry also studies the geometry of closed subvarieties of projective spaces (projective varieties).

There is also an analogue in differential geometry, projective differential geometry?, which includes the differential geometry of properties of projective spaces invariant under the projective general linear group but also more generally the study of smooth manifolds equipped with a projective connection? (a special case of a Cartan connection expressing pointwise projective geometry).

Related entries

• projective space

  • projective line

  • projective variety

  • quasiprojective variety

• synthetic projective geometry

• conic section

• cross ratio

• harmonic ratio

References

• Emil Artin, §II in: Geometric Algebra, Wiley 1957 (1988) [ISBN:978-1-118-16454-9, Wikipedia entry, ark:/13960/t4nk37034]

See also:

• Wikipedia, Projective geometry

category: geometry