Universal Log Structures on Semi-stable Varieties
نویسنده
چکیده
Fix a morphism of schemes f : X → S which is flat, proper, and “fiber-by-fiber semi-stable”. Let IV LS be the functor on the category of log schemes over S which to any T associates the isomorphism classes of pairs (MX , f), where MX is a log structure on X×S T and f : pr∗ 2MT →MX is a morphism of log structures making (X×S T ,MX)→ T a log smooth, integral, and vertical morphism. The main result of this paper is that IV LS is representable by a log scheme. In the course of the proof we also generalize results of F. Kato on the existence of log structures of embedding and semi-stable type.
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