Deformation of Brody curves and mean dimension
Deformation of Brody curves and mean dimension
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DOI：
10.1017/s014338570800076x
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发表时间：
2007-12
影响因子：
0.9
通讯作者：
M. Tsukamoto
中科院分区：
文献类型：
--
作者：
M. Tsukamoto
本文的主要目的是说明变形理论的思想可以应用于“无限维几何”。发展了Brody曲线的形变理论。Brody曲线是从复平面到射影空间的一类全纯映射。由于复平面不是紧的，变形的参数空间可以是无限维的。作为应用，我们证明了Brody曲线空间的平均维数的一个下界。
Abstract The main purpose of this paper is to show that ideas of deformation theory can be applied to ‘infinite-dimensional geometry’. We develop the deformation theory of Brody curves. A Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite-dimensional. As an application we prove a lower bound on the mean dimension of the space of Brody curves.