A parametrization of quadratic function fields whose divisor class numbers are divisible by 3 is obtained by using free parameters when the characteristics of the fields are not 3.
In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called semi-stable log structures exists if and only if the obstruction vanishes. In the case of no power, if the obstruction vanishes, then the semi-stable log structure is unique up to a unique isomorphism. So we obtain a kind of canonical structure on this family of morphisms.
