Definition 33.38.7. Let $k$ be a field. Let $X$ be a locally algebraic $k$-scheme. Let $x \in X$ be a point such that $\mathcal{O}_{X, x}$ is reduced and $\dim (\mathcal{O}_{X, x}) = 1$. The $\delta$-invariant of $X$ at $x$ is the $\delta$-invariant of $\mathcal{O}_{X, x}$ as defined in Definition 33.38.3.

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