^{n}} . A projective variety is a projective curve if its dimension is one; it is a projective surface if its dimension is two; it is a projective hypersurface...

quasi-projective variety. This is also an example of a quasi-projective variety that is neither affine nor projective. Since quasi-projective varieties generalize...

concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...

called a projective algebraic set if V = Z(S) for some S.: 9  An irreducible projective algebraic set is called a projective variety.: 10  Projective varieties...

in the projective space P(V) and its orbit under the action of G is a projective algebraic variety. This variety is a (generalized) flag variety, and furthermore...

In algebraic geometry, a weighted projective space P(a0,...,an) is the projective variety Proj(k[x0,...,xn]) associated to the graded ring k[x0,...,xn]...

embedding is used in projective geometry to consider the cartesian product (of sets) of two projective spaces as a projective variety. It is named after...

is projective, there exist nonsingular complete varieties in dimension 3 and higher which are not projective. The first examples of non-projective complete...

bundle on X is equivalent to X being a projective variety, so a Fano variety is always projective. For a Fano variety X over the complex numbers, the Kodaira...

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...