Real structures on primary Hopf surfaces

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 $H/\langle s\rangle$.