Definition:Affine Algebraic Variety

Definition

Let $k$ be a field.

Let $n \ge 1$ be an Integer.

Then a subset $X \subseteq k^n$ is an affine algebraic variety if the following hold:

$(1): \quad X$ is an affine algebraic set

$(2): \quad X$ is irreducible with respect to the Zariski topology.

Also known as

This is also called affine variety.

Also see

• Definition:Affine Scheme

Sources

• 1977: Robin Hartshorne: Algebraic Geometry $\text{I}.1$ Affine Varieties