Real structures on primary Hopf surfaces
The first goal of this article is to give a complete classification (up to Real biholomorphisms) of Real primary Hopf surfaces (H,s)\left(H,s), and, for any such pair, to describe in detail the following naturally associated objects : the group Auth(H,s){{\rm{Aut}}}_{h}\left(H,s) of Real automorphis...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2024-12-01
|
| Series: | Complex Manifolds |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/coma-2024-0007 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832593696650952704 |
|---|---|
| author | Khaled Zahraa |
| author_facet | Khaled Zahraa |
| author_sort | Khaled Zahraa |
| collection | DOAJ |
| description | The first goal of this article is to give a complete classification (up to Real biholomorphisms) of Real primary Hopf surfaces (H,s)\left(H,s), and, for any such pair, to describe in detail the following naturally associated objects : the group Auth(H,s){{\rm{Aut}}}_{h}\left(H,s) of Real automorphisms, the Real Picard group (Pic(H),sˆ*)\left({\rm{Pic}}\left(H),{\hat{s}}^{* }), and the Picard group of Real holomorphic line bundles PicR(H){{\rm{Pic}}}_{{\mathbb{R}}}\left(H). Our second goal is the classification of Real primary Hopf surfaces up to equivariant diffeomorphisms, which will allow us to describe explicitly in each case the real locus H(R)=HsH\left({\mathbb{R}})={H}^{s} and the quotient H⁄⟨s⟩H/\langle s\rangle . |
| format | Article |
| id | doaj-art-b09dcf7bd5994abd9912544e2e560ce6 |
| institution | Kabale University |
| issn | 2300-7443 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Complex Manifolds |
| spelling | doaj-art-b09dcf7bd5994abd9912544e2e560ce62025-01-20T11:08:27ZengDe GruyterComplex Manifolds2300-74432024-12-0111136738610.1515/coma-2024-0007Real structures on primary Hopf surfacesKhaled Zahraa0Department of Mathematics, Aix Marseille University, CNRS, I2M, 171 avenue de Luminy, 13009Marseille, FranceThe first goal of this article is to give a complete classification (up to Real biholomorphisms) of Real primary Hopf surfaces (H,s)\left(H,s), and, for any such pair, to describe in detail the following naturally associated objects : the group Auth(H,s){{\rm{Aut}}}_{h}\left(H,s) of Real automorphisms, the Real Picard group (Pic(H),sˆ*)\left({\rm{Pic}}\left(H),{\hat{s}}^{* }), and the Picard group of Real holomorphic line bundles PicR(H){{\rm{Pic}}}_{{\mathbb{R}}}\left(H). Our second goal is the classification of Real primary Hopf surfaces up to equivariant diffeomorphisms, which will allow us to describe explicitly in each case the real locus H(R)=HsH\left({\mathbb{R}})={H}^{s} and the quotient H⁄⟨s⟩H/\langle s\rangle .https://doi.org/10.1515/coma-2024-0007hopf surfacereal structurecomplex surface32j1532m18 |
| spellingShingle | Khaled Zahraa Real structures on primary Hopf surfaces Complex Manifolds hopf surface real structure complex surface 32j15 32m18 |
| title | Real structures on primary Hopf surfaces |
| title_full | Real structures on primary Hopf surfaces |
| title_fullStr | Real structures on primary Hopf surfaces |
| title_full_unstemmed | Real structures on primary Hopf surfaces |
| title_short | Real structures on primary Hopf surfaces |
| title_sort | real structures on primary hopf surfaces |
| topic | hopf surface real structure complex surface 32j15 32m18 |
| url | https://doi.org/10.1515/coma-2024-0007 |
| work_keys_str_mv | AT khaledzahraa realstructuresonprimaryhopfsurfaces |