Two well known results
concerning normal complex spaces are the following. First, the singular set of a
normal complex space has codimension at least two. Second, this property
characterizes normality for complex spaces which are local complete intersections.
This second result is a theorem of Abhyankar [1] which generalizes Oka’s theorem.
The purpose of this paper is to prove analogues of these facts for the class of weakly
normal complex spaces, which were introduced by Andreotti-Norguet [3] in a study of
the space of cycles on an algebraic variety. A weakly normal complex space can have
singularities in codimension one, but it will be shown that an obvious class of such
singularities is generic.
