Morphisms of varieties

Regular maps preserve algebraic structure through locally appropriate polynomial or rational expressions.

Different ways to understand it

No reviewed video yet. Explore the concept in a map or suggest a resource. Suggest a video

Coordinate rings
Polynomial functions on an affine algebraic set form a quotient by its vanishing ideal.
Projective space
Nonzero vectors modulo nonzero scalar multiplication represent projective points.
Affine varieties
Common polynomial zero sets define affine algebraic sets over a chosen field.
Algebraic dimension
Chains of prime ideals define Krull dimension and connect algebraic structure to geometric dimension.
Algebraic singularities
Singular points fail suitable smoothness conditions measured by local geometry or tangent behavior.