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relative dimension
A morphism of schemes \(f: X \rightarrow Y\) is of relative dimension \(d\) iff for all \(y \in Y\), the fiber \(X_{y}\) is equidimensional of dimension \(d\). That is, all irreducible components of \(X_{y}\) are of dimension \(d\) for any \(y\). In particular, we allow empty fibers since they have no irreducible components (an irreducible topological space is definitionally nonempty).