Vol. 68, No. 2, 1977

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An analogue of Oka’s theorem for weakly normal complex spaces

William Allen Adkins, Aldo Andreotti and John Vincent Leahy

Vol. 68 (1977), No. 2, 297–301

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.

Mathematical Subject Classification 2000
Primary: 32C20
Secondary: 32B99
Received: 20 December 1976
Published: 1 February 1977
William Allen Adkins
Aldo Andreotti
John Vincent Leahy