English

Global embeddings of weakly pseudoconvex complex spaces and refined approximation theorems

Complex Variables 2025-12-30 v2

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.

Keywords

Cite

@article{arxiv.2512.03572,
  title  = {Global embeddings of weakly pseudoconvex complex spaces and refined approximation theorems},
  author = {Yuta Watanabe},
  journal= {arXiv preprint arXiv:2512.03572},
  year   = {2025}
}

Comments

v2: 19 pages; added Examples 2.11, 2.12 and 2.13, Theorem 5.4, and Corollary 5.5. v1: 19 pages

R2 v1 2026-07-01T08:07:22.249Z