The genus of a curve discretely separates decidely different algebraic relations in two variables to focus us on the connected moduli space M g . Yet, modern applications also require a data variable (function) on the curve. The resulting spaces are versions, depending on our needs for this data variable, of Hurwitz spaces. A Nielsen class (§1.1) consists of r >- 3 conjugacy classes C in the data variable monodromy G. It generalizes the genus.
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机译：曲线的属将两个变量中决定性不同的代数关系离散地分开，以使我们关注于连接的模空间M g 。但是，现代应用程序还需要曲线上的数据变量（函数）。生成的空间是Hurwitz空间的版本，具体取决于我们对此数据变量的需求。 Nielsen类（第1.1节）由数据变量一元G中的r> -3共轭类C组成。它概括了属。
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