  Let A be the local ring at a point of a normal complex variety with
completion R. Srinivas has asked about the possible images of the induced map
from Cl A to Cl R over all geometric normal domains A with fixed completion R.
We use Noether-Lefschetz theory to prove that all finitely generated subgroups
are possible in some familiar cases. As a byproduct we show that every finitely
generated abelian group appears as the class group of the local ring at the
vertex of a cone over some smooth complex variety of each positive dimension.
