Complement to explicit description of Hopf surfaces and their automorphism groups

Abstract

In the previous paper we determined $\widetilde{\Aut}(X)$ of each Hopf surface $X = W/G$ with $W=\mathbf{C}^{2} - (0,0)$ so that its holomorphic automorphism group is given by $\Aut(X) = \widetilde{\Aut}(X)/G$. We calculate the group of connected components $\pi_{0}(\Aut(X))$ by reviewing the classification.