  The naive blow-up algebras developed by Keeler-Rogalski-Stafford, after
examples of Rogalski, are the first known class of connected graded algebras
that are noetherian but not strongly noetherian. This failure of the strong
noetherian property is intimately related to the failure of the point modules
over such algebras to behave well in families: puzzlingly, there is no fine
moduli scheme for such modules, although point modules correspond bijectively
with the points of a projective variety X. We give a geometric structure to
this bijection and prove that the variety X is a coarse moduli space for point
modules. We also describe the natural moduli stack \tilde{X} for embedded point
modules---an analog of a "Hilbert scheme of one point"---as an infinite blow-up
of X and establish good properties of \tilde{X}. The natural map \tilde{X} -> X
is thus a kind of "Hilbert-Chow morphism of one point" for the naive blow-up
algebra.
