Weak semistable reduction in characteristic 0
Weak semistable reduction in characteristic 0
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DOI：
10.1007/s002229900024
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发表时间：
1997-07
影响因子：
3.1
通讯作者：
D. Abramovich;K. Karu
中科院分区：
文献类型：
--
作者：
D. Abramovich;K. Karu
设X->；B是特征为零的簇的态射。证明了dim(B)=1(Kempf，Knudsen，Mumford，Saint-Donat)，dim(X)=dim(B)-1(De Jong)和dim(X)=dim(B)+2(Alexeev，Kollar，Shepherd-Barron)。在本文中，我们考虑一般情况。首先，我们用环面嵌入定义了半稳定态射的含义。然后，我们将变元简化为环形嵌入，并解决了半稳定约简的一个稍弱的版本。我们还用伴随的多面体复形的组合学描述了完全半稳定的约化问题。
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.