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Q-HOMOLOGY PLANES WITH C**-FIBRATIONS

Introduction. Let X be a nonsingular algebraic' surface defined over the complex number field C. We call X a homology plane (resp. a Q-homology plane) if the homology groups H^X; Z) (resp. H^X; Q)) vanish for 1 <i<4. We can also define a logarithmic homology plane X as a normal affine surface which has only quotient singularities and H{(X; Z)=0 for all />0. In our previous paper [7], Q-homology planes with Kodaira dimension less than 2 are classified and it is shown that there are many Q-homology planes which have non-trivial automorphisms of finite order. A structure theorem is given on logarithmic homology planes of Kodaira dimension — oo and 1. In particular, it is proved that a logarithmic homology plane of Kodaira dimension — oo is isomorphic to one of the following surfaces: