= Generic equidimensionality of fibres
{title2=$\dim X_y=\dim X-\dim Y$}
For a dominant <morphism of algebraic varieties> between irreducible varieties, there is a nonempty <Zariski-open subset> of the target over which every fibre is nonempty and every irreducible component has the displayed dimension. Apply <Noether normalization> to affine source charts over the target <function field> and clear denominators on the target to get a generic upper bound. Combine it with the closed-fibre lower bound in the <fiber dimension theorem>.
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