Regulärer Ring/Dimension 2/Erzwingende Algebra/Nicht drin/Affin/en/Fakt

Let $(R,𝔪)$ denote a two-dimensional regular local ring, let  $I=(f_1,\dots ,f_n)$  be an $𝔪$-primary ideal and  $f\in R$  an element with  $f\notin I$.  Let

$B=R[T_1,\dots ,T_n]/(f_1{T}_1+\cdots +f_n{T}_n+f)$

be the corresponding forcing algebra.

Then for the extended ideal $𝔪B$ we have

$H_{𝔪B}^2(B)=H^1(D(𝔪B),{𝒪}_B)=0.$

In particular, the open subset $D(𝔪B)$ is an affine scheme if and only if  $f\notin I$. 

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