Meromorphic Convexity on Complex Manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910227231670272 |
|---|---|
| author | Boudreaux, Blake J Shafikov, Rasul |
| author_facet | Boudreaux, Blake J Shafikov, Rasul |
| contents | The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of complex manifolds with a good supply of global meromorphic functions, in particular, it includes all Stein manifolds and projective manifolds. It is also shown that there exist noncompact complex manifolds, known as long $\mathbb C^2$, that are {\calligra M }-manifolds but do not contain any nonconstant holomorphic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Meromorphic Convexity on Complex Manifolds Boudreaux, Blake J Shafikov, Rasul Complex Variables 32E20 The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of complex manifolds with a good supply of global meromorphic functions, in particular, it includes all Stein manifolds and projective manifolds. It is also shown that there exist noncompact complex manifolds, known as long $\mathbb C^2$, that are {\calligra M }-manifolds but do not contain any nonconstant holomorphic functions. |
| title | Meromorphic Convexity on Complex Manifolds |
| topic | Complex Variables 32E20 |
| url | https://arxiv.org/abs/2510.27100 |