Example 49.10.5. Let $n \geq 1$ and $d \geq 1$ be integers. Let $T$ be the set of multi-indices $E = (e_1, \ldots , e_ n)$ with $e_ i \geq 0$ and $\sum e_ i \leq d$. Consider the ring

$A = \mathbf{Z}[a_{i, E} ; 1 \leq i \leq n, E \in T]$

In $A[x_1, \ldots , x_ n]$ consider the elements $f_ i = \sum _{E \in T} a_{i, E} x^ E$ where $x^ E = x_1^{e_1} \ldots x_ n^{e_ n}$ as is customary. Consider the $A$-algebra

$B = A[x_1, \ldots , x_ n]/(f_1, \ldots , f_ n)$

Denote $X_{n, d} = \mathop{\mathrm{Spec}}(A)$ and let $Y_{n, d} \subset \mathop{\mathrm{Spec}}(B)$ be the maximal open subscheme such that the restriction of the morphism $\mathop{\mathrm{Spec}}(B) \to \mathop{\mathrm{Spec}}(A) = X_{n, d}$ is quasi-finite, see Algebra, Lemma 10.123.13.

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