In higher dimensions, moduli of algebraic varieties are more difficult to construct and study.
To any irreducible algebraic variety is associated its function field.
It is used to define the dimension of an algebraic variety.
There seems to be no good way to fix this by using a finer topology on a general algebraic variety.
A quadric is thus an example of an algebraic variety.
A point of an algebraic variety which is not singular is said to be regular.
Additionally, he has made contributions to the deformation theory of algebraic varieties.
Conventions regarding the definition of an algebraic variety differ slightly.
In some sense, most algebraic varieties are of general type.
This is necessary if one wanted the quotient to be an affine algebraic variety.