Schemes: Ambient Spaces

A scheme is contained in some ambient space, either an affine space or one of a small number of standard projective spaces. It is characteristic of these spaces is that they have some kind of polynomial ring as their coordinate ring.

• Affine and projective spaces including weighted projective space
• Ruled surfaces
• Rational scrolls
• Direct products of ambient spaces
• Points of schemes with coefficients in k-algebras