Definition 95.18.2. We will denote $\mathcal{H}_ d(\mathcal{X}/\mathcal{Y})$ the *degree $d$ finite Hilbert stack of $\mathcal{X}$ over $\mathcal{Y}$* constructed above. If $\mathcal{Y} = S$ we write $\mathcal{H}_ d(\mathcal{X}) = \mathcal{H}_ d(\mathcal{X}/\mathcal{Y})$. If $\mathcal{X} = \mathcal{Y} = S$ we denote it $\mathcal{H}_ d$.

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