论文标题
表面上标记的分支投影结构的模量空间
Moduli Spaces of Marked Branched Projective Structures on Surfaces
论文作者
论文摘要
我们表明，属G属和分支N属标记的分支投射结构的模量空间是一个复杂的分析空间。在g> 1的情况下，我们表明该模量空间为6 g -6 + n，我们根据其单曲率来表征其奇异点。我们介绍了分支类别的概念，这是对分支点的分支投射结构的无限描述。我们表明，属G属和分支n的标记分支类别的空间是一个复杂的歧管。我们表明，如果N <2G-2分支射击结构的空间是分支类别空间上的仿射束，而如果n> 4G-4，前者是后者的分析子空间。
We show that the moduli space of marked branched projective structures of genus g and branching degree n is a complex analytic space. In the case g > 1 we show that this moduli space is of dimension 6 g - 6 + n and we characterize its singular points in terms of their monodromy. We introduce a notion of branching class, that is an infinitesimal description of branched projective structures at the branched points. We show that the space of marked branching classes of genus g and branching degree n is a complex manifold. We show that if n < 2g-2 the space of branched projective structures is an affine bundle over the space of branching classes, while if n > 4g-4 the former is an analytic subspace of the latter.
