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首页> 外文期刊>Annales scientifiques de l'Ecole normale superieure >FOLIATED STRUCTURE OF THE KURANISHI SPACEAND ISOMORPHISMS OF DEFORMATION FAMILIESOF COMPACT COMPLEX MANIFOLDS
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FOLIATED STRUCTURE OF THE KURANISHI SPACEAND ISOMORPHISMS OF DEFORMATION FAMILIESOF COMPACT COMPLEX MANIFOLDS

机译：Kuranishi空间的叶结构和变形族紧凑复杂流形的同构。

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摘要

Consider the following uniformization problem. Take two holomorphic (parame-trized by some analytic set defined on a neighborhood of 0 in C~P, for some p > 0) or differentiable (parametrized by an open neighborhood of 0 in R~P, for some p > 0) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point t of the parameter space, the fiber over t of the first family is biholomorphic to the fiber over t of the second family. Then, under which conditions are the two families locally isomorphic at 0? In this article, we give a sufficient condition in the case of holomorphic families. We show then that, surprisingly, this condition is not sufficient in the case of differentiable families. We also describe different types of counterexamples and give some elements of classification of the counterexamples. These results rely on a geometric study of the Kuranishi space of a compact complex manifold.
机译：考虑以下均匀化问题。取两个全同（在C〜P中定义为0的解析集进行参数化，对于某些p> 0）或可微分（在R〜P中定义为0的开放邻域，对于某些p> 0）进行变形紧凑型复杂流形的系列。假设它们是逐点同构的，即对于参数空间的每个点t，第一个族的t上的光纤与第二个族的t上的光纤是全同构的。那么，在什么条件下两个族在0处局部同构？在本文中，我们给出了全纯族的充分条件。令人惊讶的是，我们证明了这种情况对于有区别的家庭来说是不够的。我们还描述了不同类型的反例，并给出了一些反例的分类要素。这些结果依赖于一个紧凑的复杂流形的Kuranishi空间的几何研究。

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