Definition 29.29.1. Let $f : X \to S$ be a morphism of schemes. Assume $f$ is locally of finite type.

1. We say $f$ is of relative dimension $\leq d$ at $x$ if $\dim _ x(X_{f(x)}) \leq d$.

2. We say $f$ is of relative dimension $\leq d$ if $\dim _ x(X_{f(x)}) \leq d$ for all $x \in X$.

3. We say $f$ is of relative dimension $d$ if all nonempty fibres $X_ s$ are equidimensional of dimension $d$.

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