Isometric Families of Kähler Structures
Isometric Families of Kähler Structures
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Kähler 结构的等距族
DOI：
10.1007/978-1-4613-8109-9_3
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发表时间：
1980
期刊：
影响因子：
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通讯作者：
E. Calabi
中科院分区：
文献类型：
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作者：
E. Calabi
本研究的动机是确定和描述固定的实流形上任何给定的复解析结构族的经典问题，松散地说，该子族由代数流形组成。这个问题可能是不可能完全通用性的，即使正确地陈述了它缺少的限定条件，这里在一个非常有限的情况下处理，其中所考虑的族的每个复杂结构都允许Kahler度量，使得同一族的复流形是等距的(尽管在一般的分析上并不复杂)。显然，与一般问题相比，这种情况具有很高的限制性；然而，人们可以从这两类典型的等距族中提取的信息提供了一些关于非代数簇的某些模空间的全局结构的有趣结果，例如K3曲面、复环面和一种特殊类型的2n维有理仿射簇。
The present study is motivated by the classical problem, loosely stated, of determining and describing, for any given family of complex analytic structures on a fixed, underlying real manifold, which subfamily consists of algebraic manifolds. This problem, which is probably inaccessible in its full generality, even when correctly stated with its missing qualifications, is treated here in a very restricted case, where each of the complex structures of the families under consideration admits a Kahler metric, such that the complex manifolds of the same family are isometric (though not complex analytically, in general). Clearly, this situation is highly restrictive compared to the general problem; however the information that one can extract from the two typical classes of such isometric families that can occur provides some interesting results on the global structure of some moduli spaces of nonalgebraic varieties, such as the K3-surfaces, the complex tori, and a special type of 2n-dimensional, rational affine variety.