Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916047833006080 |
|---|---|
| author | Rond, Guillaume |
| author_facet | Rond, Guillaume |
| contents | We answer in the negative the long-standing open question of whether biholomorphic equivalence implies algebraic equivalence for germs of real algebraic manifolds in $\mathbb C^n$. More precisely we give an example of two germs of real algebraic surfaces in $\mathbb C^2$ that are biholomorphic, but not by means of an algebraic biholomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent Rond, Guillaume Complex Variables Algebraic Geometry Combinatorics 32H02, 13F25, 14P05, 32C05, 32V40, 39B32 We answer in the negative the long-standing open question of whether biholomorphic equivalence implies algebraic equivalence for germs of real algebraic manifolds in $\mathbb C^n$. More precisely we give an example of two germs of real algebraic surfaces in $\mathbb C^2$ that are biholomorphic, but not by means of an algebraic biholomorphism. |
| title | Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent |
| topic | Complex Variables Algebraic Geometry Combinatorics 32H02, 13F25, 14P05, 32C05, 32V40, 39B32 |
| url | https://arxiv.org/abs/2503.08957 |