  Recent works of the authors have demonstrated the usefulness of considering
moduli spaces of Artinian reductions of a given ring when studying standard
graded rings and their Lefschetz properties. This paper illuminates a key
aspect of these works, the behaviour of the canonical module under deformations
in this moduli space. We demonstrate that even when there is no natural
geometry around, we can give a viewpoint that behaves like it, effectively
constructing geometry out of nothing, giving interpretation to intersection
numbers without cycles. Moreover, we explore some properties of this
normalization.
