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  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  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. © 1977 Pacific Journal of Mathematics. All rights reserved.
Publication Source (Journal or Book title)
Pacific Journal of Mathematics
Adkins, W., Andreotti, A., & Leahy, J. (1977). An analogue of oka’s theorem for weakly normal complex spaces. Pacific Journal of Mathematics, 68 (2), 297-301. https://doi.org/10.2140/pjm.1977.68.297