We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus \(g\ge 2\), which preserve the holonomy representation of the structure and the order of the branch points. In the case of non-elementary holonomy we show that when the underlying complex structure is infinitesimally preserved the branch points are necessarily arranged on a canonical divisor, and we establish a partial converse for hyperelliptic structures.

中文翻译：

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分支投影结构的局部变形：Schiffer变体和Teichmüller贴图

我们研究了一类\（g \ ge 2 \）闭合表面上分支复杂投影结构的连续变形，该变形保持结构的完整表示和分支点的顺序。在非基本完整的情况下，我们表明当无限复杂地保留下面的复杂结构时，分支点必定排列在规范的除数上，并且我们建立了超椭圆结构的部分逆。