  Let V be a smooth quasi-projective complex surface such that the three first
logarithmic plurigenera are equal to 1 and the logarithmic irregularity is
equal to 2. We prove that the quasi-Albanese morphism of V is birational and
there exists a finite set S such that the quasi-Albanese map is proper over the
complement of S in the quasi-Albanese variety A(V) of V. This is a sharp
effective version of a classical result of Iitaka.
