deCone(A, x)
deCone(A, i)
The decone of a central arrangement $A$ at a hyperplane $H=H_i$ or $H=\ker x$ is the affine arrangement obtained from $A$ by first deleting the hyperplane $H$ then intersecting the remaining hyperplanes with the (affine) hyperplane $\{x=1\}$. In particular, if $R$ is the coordinate ring of $A$, then the coordinate ring of its decone over $x$ is $R/(x-1)$.
The decone of a central arrangement at $H$ can also be constructed by first projectivizing $A$, then removing the image of $H$, and identifying the complement of $H$ with affine space.
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The coordinate ring of $dA$ is $\mathbb{Q}[x_1,x_2,x_3]/(x_3-1)$.
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Use prune to get something whose coordinate ring is a polynomial ring.
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