Weak semistable reduction in characteristic 0
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
Let X->B be a morphism of varieties in characteristic zero. Semistable reduction has been proved for dim(B)=1 (Kempf, Knudsen, Mumford, Saint-Donat), dim(X)=dim(B)-1 (de Jong) and dim(X)=dim(B)+2 (Alexeev, Kollar, Shepherd-Barron). In this paper we consider the general case. First we define what we mean by a semistable morphism in terms of toroidal embeddings. Then we reduce the varieties to toroidal embeddings and solve a slightly weaker version of semistable reduction. We also state the full semistable reduction problem in terms of combinatorics of the associated polyhedral complexes.
Keywords
Cite
@article{arxiv.alg-geom/9707012,
title = {Weak semistable reduction in characteristic 0},
author = {Dan Abramovich and Kalle Karu},
journal= {arXiv preprint arXiv:alg-geom/9707012},
year = {2008}
}
Comments
AMS-LaTeX, 22 pages