Global embeddings of weakly pseudoconvex complex spaces and refined approximation theorems

TL;DR

This paper refines approximation theorems for holomorphic sections to embed weakly pseudoconvex complex spaces with positive line bundles into projective space, solving the Union problem for such manifolds.

Contribution

It introduces refined approximation theorems that enable embedding weakly pseudoconvex complex spaces into projective space, advancing complex geometry techniques.

Findings

Regular locus can be embedded into projective space

Union problem is solvable for weakly pseudoconvex manifolds

Refined approximation theorems are established

Abstract

In this paper, by refining approximation theorems for holomorphic sections of adjoint line bundles, it is proved that the regular locus of a weakly pseudoconvex complex space admitting a positive line bundle can be holomorphically embedded into a complex projective space. As an application of approximation theorems, it is shown that the Union problem can be solved for weakly pseudoconvex manifolds.