Real structures on primary Hopf surfaces

TL;DR

This paper classifies Real primary Hopf surfaces up to biholomorphism and equivariant diffeomorphism, detailing their automorphisms, Picard groups, and real loci, providing a comprehensive understanding of their geometric and topological structures.

Contribution

It provides a complete classification of Real primary Hopf surfaces and describes associated automorphism groups, Picard groups, and real loci in detail.

Findings

Complete classification of Real primary Hopf surfaces

Explicit descriptions of automorphism and Picard groups

Analysis of real loci and quotients

Abstract

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