Log smooth deformation theory
type: Item
instance of: scholarly article
title: Log smooth deformation theory
zbMATH Open document ID: 0876.14007
author: Fumiharu Kato
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1997-12-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/alg-geom/9406004
review text: This paper lays a foundation for 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 on it, and (2) global smoothings of normal crossing varieties. The former is a generalization of the relative deformation theory introduced by \textit{Makio} and others, and the latter coincides with the logarithmic deformation theory introduced by Kawamata and Namikawa.
Mathematics Subject Classification ID: 14D15
Mathematics Subject Classification ID: 13D10
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 1044116
zbMATH Keywords: log smooth deformation functor
zbMATH Keywords: relative deformations
zbMATH Keywords: global smoothings
MaRDI profile type: Publication
OpenAlex ID: W2121235894
arXiv ID: alg-geom/9406004
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DOI: 10.2748/TMJ/1178225336
description: scientific article