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.
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