On saturation and the model theory of compact Kähler manifolds
On saturation and the model theory of compact Kähler manifolds
复制标题
饱和度与紧Kähler流形的模型理论
DOI：
10.1515/crll.2005.2005.586.1
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Rahim Moosa
中科院分区：
文献类型：
--
作者：
Rahim Moosa
摘要提出了一个假设，在这个假设下，紧复解析空间X作为解析集语言中的一个结构，本质上是饱和的。证明了当X的所有笛卡尔幂的受限Douady空间的不可约分量都紧致时，才满足这个条件。通过一个藤木定理，讨论了Kähler-type空间上满足上述条件的饱和的一些含义。特别地，我们得到了在Kähler-type空间类中存在相对代数约简这一事实的模型理论证明。
Abstract A hypothesis is introduced under which a compact complex analytic space, X, viewed as a structure in the language of analytic sets, is essentially saturated. It is shown that this condition is met exactly when the irreducible components of the restricted Douady spaces of all the cartesian powers of X are compact. Some implications of saturation on Kähler-type spaces, which by a theorem of Fujiki meet the above condition, are discussed. In particular, one obatins a model-theoretic proof of the fact that relative algebraic reductions exist in the class of Kähler-type spaces.