Editing Projective space (section)

=== Scheme theory ===
Scheme theory, introduced by [[Alexander Grothendieck]] during the second half of 20th century, allows defining a generalization of algebraic varieties, called [[scheme (mathematics)|schemes]], by gluing together smaller pieces called [[affine schemes]], similarly as [[manifold]]s can be built by gluing together open sets of {{math|'''R'''<sup>''n''</sup>}}.  The [[Proj construction]] is the construction of the scheme of a projective space, and, more generally of any projective variety, by gluing together affine schemes. In the case of projective spaces, one can take for these affine schemes the affine schemes associated to the charts (affine spaces) of the above description of a projective space as a manifold.
{{See also|Algebraic geometry of projective spaces}}