projective space

All of the above holds for complex projective space, too.

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

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

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

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

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

The above definition of projective space gives a set.

All line bundles on complex projective space can be obtained by the following construction.

Its closure in projective space is the rational normal curve.

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

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

The projective space case is included: see tautological line bundle.

It is not much harder to do n dimensional projective space.

One may formalize this using various ways of presenting a projective space.

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

In particular such a product of real projective spaces is not null-cobordant.

It is generally assumed that projective spaces are of at least dimension 2.

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

This is not the canonical bundle of the projective space as defined above.

The following result is an astonishing statement for finite projective spaces.

Complex projective space has many applications in both mathematics and quantum physics.

Projective spaces provide some more interesting examples of principal bundles.

Its general projection to three-dimensional projective space is called a Steiner surface.

This description generalizes to complex projective space of higher dimension.

These real projective spaces can be constructed in a slightly more rigorous way as follows.