The Stacks project

Definition 81.2.5. In Situation 81.2.1 for any good $X/B$ and any irreducible closed subset $T \subset |X|$ we define

\[ \dim _\delta (T) = \delta (\xi ) \]

where $\xi \in T$ is the generic point of $T$. We will call this the $\delta $-dimension of $T$. If $T \subset |X|$ is any closed subset, then we define $\dim _\delta (T)$ as the supremum of the $\delta $-dimensions of the irreducible components of $T$. If $Z$ is a closed subspace of $X$, then we set $\dim _\delta (Z) = \dim _\delta (|Z|)$.


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