Classification of three-dimensional flips
Classification of three-dimensional flips
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DOI：
10.1090/s0894-0347-1992-1149195-9
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发表时间：
1992-09
影响因子：
3.9
通讯作者：
J. Kollár;S. Mori
中科院分区：
文献类型：
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作者：
J. Kollár;S. Mori
这个定理的重要性在于，尽管我们引入了一些奇点，但簇X‘应该被认为比X简单得多。事实上，X’是X的二元等价类中最简单的簇。因此，如果我们想要研究X在二元变换下不变的性质，那么我们应该考虑X‘上的这些性质。这种方法导致了几个深结构定理的证明(例如，参见最近的一次调查[Kolhir91，第3章])。本文的目的是研究家庭中的上述过程。更准确地说，假设{XI：t E~}是光滑的单参数平坦族
The importance of this theorem is that despite the fact that we introduce some singularities, the variety X'should be considered as much simpler than X. In fact X'is the simplest variety within the birational equivalence class of X. Thus if we want to study properties of X which are invariant under birational transformations then we should consider these properties on X'. This approach leads to the proof of several deep structure theorems (see, eg,[Kolhir91, Chapter 3] for a recent survey). The aim of this article is to study the above process in families. To be more precise, assume that {XI: t E~} is a one-parameter flat family of smooth