The moduli space of Hopf surfaces (Q1906583)

The authors study the moduli space of complex structures on \(S^1 \times (S^3/H)\), where \(H \subset U(2)\) is a finite abelian group acting properly discontinuous and free on \(S^3\). The main result is that for \(H\) not cyclic, the fine moduli space for all complex structures on \(S^1 \times (S^3/H)\) exists. For \(H\) cyclic, it does not. The method used is by direct computation of the dimension of \(H^1(V, \Theta)\).