Log Smooth Deformation Theory

Details Log Smooth Deformation Theory Log Smooth Deformation Theory

1994-06-15

arxiv.org/abs/alg-geom/9406004v3

Mathematics

Algebraic Geometry

29 pages, Latex version 2.09, Kyoto-Math 94-07

Scientific paper

This paper gives a foundation of log smooth deformation theory. We study the infinitesimal liftings of log smooth morphisms and show that the log smooth deformation functor has a representable hull. This deformation theory gives, for example, the following two types of deformations: (1) relative deformations of a certain kind of a pair of an algebraic variety and a divisor of it, and (2) global smoothings of normal crossing varieties. The former is a generalization of the relative deformation theory introduced by Makio, and the latter coincides with the logarithmic deformation theory introduced by Kawamata and Namikawa.

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