Moduli of marked Riemann surfaces
Moduli of marked Riemann surfaces
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标记黎曼曲面的模
DOI：
10.1090/s0002-9904-1974-13600-1
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
B. Maskit
中科院分区：
文献类型：
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作者：
B. Maskit
本注记的目的是展示亏格为g§^2的闭黎曼曲面空间的一组复解析模，以基本群的基为标记。我们可以找到这样的模数（即，Bers [2]证明了亏格g的Teichmüller空间在C ~*）中是双全纯嵌入的.他的模量是变化的，它们取决于基面的选择。我们的模量在某种意义上是内在的，类似于Fenchel-Nielsen [4]和Keen [5]的（真实的）模量。事实上，我们的模量应被视为复杂的类似物的Fenchel-Nielsen和基恩模量。(The这些不同模量之间的几何关系是清楚的，并且它们是实解析等价的。下面给出的模的实际表达式涉及乘法常数和平方根。这些标准化有两个目的。首先，模空间包含在半平面的乘积中。其次，通过这些规范化，
The purpose of this note is to exhibit a set of complex analytic moduli for the space of closed Riemann surfaces of genus g§^2, marked by a basis for the fundamental group. That one could find such moduli (i.e., biholomorphically embed the Teichmüller space of genus g in C*~) was proven by Bers [2]. His moduli are variational—they depend on a choice of base surface. Our moduli are in some sense intrinsic, similar to the (real) moduli of Fenchel-Nielsen [4] and Keen [5]. In fact our moduli should be regarded as the complex analogue of the Fenchel-Nielsen and Keen moduli. (The geometric relationship between these different moduli is clear, and they are real-analytically equivalent.) The actual expressions for the moduli given below involve multiplicative constants and square roots. These normalizations serve two purposes. First, the moduli space is contained in a product of half-planes. Second, with these normalizations, the group of translations