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This is my PhD Thesis, part of it has published in Acta Mathematica Sinica.In this paper, a class of morphisms which have a kind of singularity weakerthan normal crossing is considered. We construct the obstruction such that theso-called semi-stable log structures exists if and only if the obstructionvanishes. In the case of no power, if the obstruction vanishes, then thesemi-stable log structure is unique up to a unique isomorphism. So we obtain akind of canonical structures on this family of morphisms.

Log Structures on Generalized Semi-Stable Varieties