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date: 2022-03-22 21:23
modification date: Tuesday 22nd March 2022 21:23:44
title: relative dimension
aliases: [relative dimension]

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- Tags 
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- Refs:
	- #todo/add-references
- Links:
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# relative dimension

A morphism of [schemes](Unsorted/scheme.md) $f: X \rightarrow Y$ 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).