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2003 Universal log structures on semi-stable varieties
Martin C. Olsson
Tohoku Math. J. (2) 55(3): 397-438 (2003). DOI: 10.2748/tmj/1113247481


Given a morphism of schemes which is flat, proper, and "fiber-by-fiber semi-stable'', we study the problem of extending the morphism to a morphism of fine log schemes, which is log smooth, integral, and vertical. The problem is rephrased in terms of a functor on the category of fine log schemes over the base, and the main result of the paper is that this functor is representable by a fine log scheme whose underlying scheme maps naturally to the base by a monomorphism of finite type. In the course of the proof, we also generalize results of Kato on the existence of log structures of embedding and semi-stable type.


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Martin C. Olsson. "Universal log structures on semi-stable varieties." Tohoku Math. J. (2) 55 (3) 397 - 438, 2003.


Published: 2003
First available in Project Euclid: 11 April 2005

zbMATH: 1069.14015
MathSciNet: MR1993863
Digital Object Identifier: 10.2748/tmj/1113247481

Primary: 14D22
Secondary: 14H10, 14M25

Rights: Copyright © 2003 Tohoku University


Vol.55 • No. 3 • 2003
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