A New Class of Domains of Holomorphy (II). Domains of holomorphy on a three dimensional Stein space with an isolated singularity

The present paper is the continuation of O. Suzuki [10]. There we defined the concept of L-manifolds (see Definition (3.11) in O. Suzuki [10]) and showed that every L-manifold is a domain of holomorphy in the sense of H. Kerner [7] (see Definition (2.5) in O. Suzuki [10]). Moreover, we showed that there exist L-manifolds which are neither holomorphically convex nor pseudoconvex manifolds and there exist Lmanifolds which admit non-Stein algebras (see Definition (3.15) in O. Suzuki [10]). These results are summarized in Theorems I and II in Introduction in O. Suzuki [10]. Unfortunately, only two examples are given there. In this paper we shall prove that under the condition (A) certain domains of holomorphy (which will be called simple domains) on a certain three dimensional Stein space with an isolated singularity are in fact L-manifolds. By this we can systematically construct many examples of domains of holomorphy which are not Stein manifolds. Let M be a Stein space with an isolated singularity p0. As will be shown in §3, every domain of holomorphy A_ which does not contain pQ as a boundary point is a Stein space. But in the case where p0 e dA_9 the situation is not simple. There we can find many domains of