 Dominant morphism of affine varieties (source code)

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= Dominant morphism of affine varieties

A morphism $f:X\to Y$ of affine varieties is dominant when its image is <Zariski dense> in $Y$. It is dominant exactly when the pullback homomorphism
$$
f^*:k[Y]\to k[X]
$$
is injective. When $X$ and $Y$ are irreducible, this injection extends to their function fields and gives $\dim X\geq\dim Y$.

This is the dense-image case of a <morphism of algebraic varieties>.

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