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I'm not so strong good on the scheme-theoretic language, so let me embed $F_n$ as the affine variety $latex \text{res}{n,n}(X^n \text{res}_{n,n}(X^n + ..., b{n-1} b_{n-1} X^{n-1} + ...) y = 1$ in one dimension up. Then a morphism $\text{Spec } k[a_0, k[a_0, ... a_{n-1}, b_0, ... b_{n-1}, y]$y]/(\text{stuff}) \to R$is precisely (assuming that Cazanava means either$k = \mathbb{Z}$or$R$a$k$-algebra) a choice, for each variable$a_i, b_i, y$, of an element of$R$subject to the condition that the resultant times$y$is equal to$1$, i.e. the resultant is invertible in$R\$.