English

Real structures on primary Hopf surfaces

Complex Variables 2023-12-05 v2 Differential Geometry

Abstract

The first goal of this article is to give a complete classification (up to Real biholomorphisms) of Real primary Hopf surfaces (H,s)(H,s), and, for any such pair, to describe in detail the following naturally associated objects : the group Auth(H,s)\mathrm{Aut}_h(H,s) of Real automorphisms, the Real Picard group (Pic(H),s^)(\mathrm{Pic}(H),\hat s^*), and the Picard group of Real holomorphic line bundles PicR(H)\mathrm{Pic}_{\mathbb{R}}(H). Our second goal: 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(\mathbb{R})=H^s and the quotient H/sH/\langle s\rangle.

Keywords

Cite

@article{arxiv.2310.05265,
  title  = {Real structures on primary Hopf surfaces},
  author = {Zahraa Khaled},
  journal= {arXiv preprint arXiv:2310.05265},
  year   = {2023}
}
R2 v1 2026-06-28T12:44:02.233Z