We characterize the representations of the fundamental group of a closed surface to $\text{◂⋅▸}{\mathrm{PSL}}_2(\mathbb{C})$ that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the holonomies of the spherical metrics with prescribed integral conical angles and the holonomies of affine structures with fixed conical angles on closed surfaces.

中文翻译：

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具有指定分支数据的曲面上复杂射影结构的整体性

我们将闭曲面的基本群的表示特征化为$\text{◂⋅▸}{\mathrm{PSL}}_{\mathrm{2个}}(\mathbb{C})$作为具有固定分支除数的分支复射影结构的整体性出现。特别是，我们计算了具有指定积分圆锥角的球面度量的完整度和封闭曲面上具有固定圆锥角的仿射结构的完整度。