English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

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

A new class of domains of holomorphy. II. Domains of holomorphy on a three dimensional Stein space with an isolated singularity