论文标题
复杂仿射和扩张表面的模量空间
Moduli spaces of complex affine and dilation surfaces
论文作者
论文摘要
我们构建复杂仿射和扩张表面的模量空间。使用Veech的想法，我们表明，具有固定属的仿射表面的模量空间，并具有固定复杂顺序的圆锥点，是Riemann表面模量空间上的全态仿射束。同样，扩张表面的模量空间是Riemann表面模量空间的覆盖空间。我们对扩张表面的模量空间的连接组件进行了分类，并表明任何组件都是Orbifold K（g，1），其中G是Calderon-Salter的构图映射类组。
We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech, we show that the the moduli space of affine surfaces with fixed genus and with cone points of fixed complex order is a holomorphic affine bundle over the moduli space of Riemann surfaces. Similarly, the moduli space of dilation surfaces is a covering space of the moduli space of Riemann surfaces. We classify the connected components of the moduli space of dilation surfaces and show that any component is an orbifold K(G,1) where G is the framed mapping class group of Calderon-Salter.
