algebraic variety

In some sense, most algebraic varieties are of general type.

A quadric is thus an example of an algebraic variety.

It is used to define the dimension of an algebraic variety.

It is analogous to the included concept of real or complex algebraic variety.

To any irreducible algebraic variety is associated its function field.

Conventions regarding the definition of an algebraic variety differ slightly.

A point of an algebraic variety which is not singular is said to be regular.

In higher dimensions, moduli of algebraic varieties are more difficult to construct and study.

Suppose that X is a smooth complex algebraic variety.

This is necessary if one wanted the quotient to be an affine algebraic variety.

Additionally, he has made contributions to the deformation theory of algebraic varieties.

Invariant theory - studies how group actions on algebraic varieties affect functions.

A regular map between complex algebraic varieties are holomorphic maps.

It has been related to correspondences of algebraic varieties.

There seems to be no good way to fix this by using a finer topology on a general algebraic variety.

A variety of algebras should not be confused with an algebraic variety.

In more abstract language, it is a general result on the equations defining Grassmannians as algebraic variety.

The origin in the algebraic variety defined by is a simple normal crossings singularity.

The special set in an algebraic variety is the subset in which one might expect to find many rational points.

Algebraic varieties differ widely in how many birational automorphisms they have.

Note that the two terms algebraic variety and variety of algebra should not be confused.

Regular maps are, by definition, morphisms in the category of algebraic varieties.

In mathematics, a pseudo-canonical variety is an algebraic variety of "general type".

Complex algebraic varieties (even with singularities) are examples of pseudomanifolds.

An algebraic curve is an algebraic variety of dimension one.