The zeros form a cubic surface in 3-dimensional projective space.

By the same construction, projective spaces can be considered in higher dimensions.

Its direct construction is as a special case of the projective space over a division algebra.

Complex projective spaces Since is simply connected, such a structure has to be unique.

We begin with a preliminary on a morphism into a projective space.

Indeed, we can assume X is the projective space by the early discussion.

It is often desirable to consider curves in the projective space.

Part of a conventional projective space is collapsed down to a point.

So we can say that most smooth hypersurfaces in projective space are of general type.

The above definition of projective space gives a set.