Inoue Surfaces With b2 = 0
Inoue introduced three families of surfaces, S0, S+ and S−, which are compact quotients of (a product of a complex plane by a half-plane). These Inoue surfaces are solvmanifolds. They are obtained as quotients of by a solvable discrete group which acts holomorphically on .
The solvmanifold surfaces constructed by Inoue all have second Betti number . These surfaces are of Kodaira class VII, which means that they have and Kodaira dimension . It was proven by Bogomolov, Li-Yau and Teleman that any surface of class VII with b2 = 0 is a Hopf surface or an Inoue-type solvmanifold.
These surfaces have no meromorphic functions and no curves.
K. Hasegawa gives a list of all complex 2-dimensional solvmanifolds; these are complex torus, hyperelliptic surface, Kodaira surface and Inoue surfaces S0, S+ and S−.
The Inoue surfaces are constructed explicitly as follows.
Read more about this topic: Inoue Surface
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