Open algebraic surfaces with logarithmic Kodaira dimension zero.

Let S be a smooth rational open algebraic surface whose logarithmic Kodaira dimension and logarithmic geometric genus are zero. In this talk, I construct a strongly minimal model (V,D) of S and determine the pair (V,D) when S has non-contractible boundary at infinity. By using the classification result, I give some results on the structure of log affine surfaces with logarithmic Kodaira dimension zero.