= Projective coordinates over a local ring
{title2=$\operatorname{Hom}(\operatorname{Spec}A,\mathbb P^n)=\{(a_i):\exists i,\ a_i\in A^\times\}/A^\times$}
For a <local ring> $A$, every map from $\operatorname{Spec}A$ into <projective space> lands in one standard chart: the inverse image of a chart containing the closed point is the whole spectrum. This gives <homogeneous coordinates> with at least one unit entry, unique up to a common <unit>. For a nonlocal ring, coordinates may instead merely generate the unit ideal, and general maps can involve a nontrivial <invertible sheaf> quotient.
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